SYRIAN President Hafez al-Assad has one simple, overriding purpose in attending a peace conference with Israel: to recover the Golan Heights.Syria lost this 500-square-mile upland region, perched on hills overlooking the Sea of Galilee, in the 1967 Six-Day war. With it, Damascus lost a key strategic advantage in its conflict with the Jewish state. At the outset of the 1973 Arab-Israeli war, Syrian troops seized the heights in a lightning attack, and the Israelis regained control over the area only after bitter fighting. Since then, Israel has annexed the Golan Heights and turned it into one of the world's most thickly fortified and heavily defended pieces of land. The presence of Israeli troops just 30 miles from Damascus, on traditionally Syrian territory, has long humiliated Mr. Assad. Until recently, his strategy for recovering the Golan had been based on achieving military parity with Israel in order to build a stronger negotiating position or else have the option of a 1973-style assault. But the collapse of Syria's principal source of arms, the Soviet Union, has rendered that policy unworkable. Now Assad is pinning his hopes on United States promises that he may be able to regain the Golan in exchange for working out a peace agreement with the Israelis. Although opposed by Israel, the emergence of such a solution from the latter stages of the talks could test Assad's commitment to the Palestinian cause. If Palestinian claims to a homeland are rebuffed, Assad may have to decide whether to support his Arab brethren or proceed toward his own, separate peace with Israel. Syria also has an interest in the outcome of talks between its prot, Lebanon, and Israel, which controls a so-called security zone in southern Lebanon. The Syrian and Lebanese governments want to see an Israeli withdrawal, but Israel is refusing to relinquish its control without a parallel withdrawal of Syrian troops from Lebanese soil, and security guarantees along its northern border.