THE immediate problem facing Japan's new coalition Government, now that it has reached agreement on its programme for political reform, is what will be the reaction of the opposition Liberal Democratic Party (LDP). The reform issue is a crucial test for newly-installed LDP leader Yohei Kono since, if he mishandles it, the once-dominant party could split, thereby further complicating the fast-changing Japanese political scene. The LDP reaction is critical because it remains the largest single party in the Japanese parliament and has already shown a disposition to be obstructive, as when it delayed the formation of the new administration led by Prime Minister Morihiro Hosokawa. Since Mr Hosokawa has said he will ''take responsibility'' for securing the parliamentary passage of political reform by the end of 1993, the LDP may be willing to filibuster the bill until the end of the year, in the hope that this will force the Prime Minister to resign. A basic problem is that there is no tradition of a government routinely using its majority to pass its own bills. At least four government bills will be required to encompass the various reform measures, and these are due to be presented to the next parliamentary session, which begins on September 17. Thus the opportunity exists for the LDP to bring that session to a complete halt if it refuses to co-operate in the passage of the reform bills. A large number of LDP MPs still argue against all reform and prefer to keep the present system of multi-member seats. Yet another viewpoint prefers single-seat constituencies only in the next Lower House election, without any proportional representation. A generational conflict within the LDP became evident when Mr Kono defeated veteran LDP factional leader Michio Watanabe in the recent leadership ballot. Hence the acute pressures on Mr Kono. If he opts for the path of obstruction and delaying tactics, he could end up offending the younger reform-minded elements within the party, who are already openly talking about the LDP breaking up. If he heeds the plea of Chief Cabinet Secretary Masayoshi Takemura, and opts for agreeing to, or at least not obstructing, the coalition's reform programme, then he may be seen as weak and expendable by the older generation, who would have preferred Mr Watanabe in the first place. Mr Kono will probably try both tactics. He may initially start off by trying to secure government agreement to change the ratio of constituency seats to proportional representation back to 300 and 200 respectively. It has even been suggested that he should argue for 550 seats, with 350 in constituencies and 200 in proportional representation. Protracted negotiations could test the coalition, which will be unable to give in to Mr Kono's demands for fear of alienating the largest coalition party, the Socialists. But, in the end, Mr Kono will probably find supporting the reform bills less risky, since the reform-minded LDP MPs are the ones most likely to quit the party if frustrated with its prospects. An extended stalemate in parliament over reform could end what the Japanese call ''the 1955 system''. In 1955 both the LDP and the Socialists were formed out of previously rival factions. There are some who expect both the LDP and the Socialist Party to disappear, in their present forms, before the end of next year.