
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
When substituting in Chebyshev polynomials (see problem 61099) the value \( x = \cos \alpha \), the results are \( T_{n}(\cos \alpha) = \cos n \alpha \) and \( U_{n-1}(\cos \alpha) = \frac{\cos n \alpha}{\cos \alpha} \).

What will happen if the value \( x = \sin \alpha \) is substituted into the Chebyshev polynomials?

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