
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  $\triangle ABC$  satisfies  $\cos A:\cos B:\cos C=1:1:2$ , then  $\sin A=\sqrt[s]{t}$ ( $s\in\mathbb{N},t\in\mathbb{Q^+}$  and  $t$  is an irreducible fraction). Find  $s+t$ .

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