
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 $0 < \alpha < \frac{\pi}{2}$ and $\log(1+\cos\alpha) = m$, $\log\left(\frac{1}{1-\cos\alpha}\right) = n$, then $\log(\sin\alpha) =$ ______? (Express your answer in terms of $m$ and $n$)

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