
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given in $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. The following four conditions are provided:
(1) $\tan(A-B) \cos C = 0$; (2) $\sin(B+C) \cos(B-C) = 1$; (3) $a\cos A = b\cos B$; (4) $\sin^2(A-B) + \cos^2 C = 0$.
If the condition is satisfied, then $\triangle ABC$ is an isosceles right triangle. (Only one serial number needs to be filled in)

Present the answer in LaTex format: \boxed{Your answer}
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