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fix(tools): put tool_search promotions on the next infer wire #2447

Job	Run time
static-analysis	46s
test (2/4)	1m 59s
test (3/4)	41s
test (4/4)	34s
test (1/4)	47s
build	10s
test (one-process pollution detector)	0s
eslint	4s
prettier	3s
typecheck	3s
build-and-test	4s
test (src)	2s
	5m 13s