
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
\[ 
8.477 \frac{1+\sin x+\sin^{2} x+\ldots+\sin^{n} x+\ldots}{1-\sin x+\sin^{2} x-\ldots+(-1)^{n} \sin^{n} x+\ldots} = \frac{4}{1+\operatorname{tg}^{2} x}, \quad |\sin x| \neq 1 
\]

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