
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]


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Find the generating functions for the sequences of Chebyshev polynomials of the first and second kinds:

$$
F_{T}(x, z)=\sum_{n=0}^{\infty} T_{n}(x) z^{n} ; \quad F_{U}(x, z)=\sum_{n=0}^{\infty} U_{n}(x) z^{n}
$$

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