
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
Simplify:

1. \(\sin 5 A - 5 \sin 3 A + 10 \sin A\)
2. \(1 + C_{n}^{1} \cos x + C_{n}^{2} \cos 2x + C_{n}^{3} \cos 3x + \cdots + C_{n}^{n} \cos nx \quad \left(n \in \mathbf{N}^{*}\right)\)

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