
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
Let $A$, $B$, and $C$ be the three interior angles of $\triangle ABC$. Among the following relationships, the one that always holds true is ______ (fill in the number).

$(1) \cos(A+B) = \cos C$

$(2) \cos \left( \frac{B+C}{2} \right) = \sin \left( \frac{A}{2} \right)$

$(3) \sin(2A+B+C) = -\sin A$

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