
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
Form an equation whose roots are the numbers:
a) $\sin ^{2} \frac{\pi}{2 n+1}, \sin ^{2} \frac{2 \pi}{2 n+1}, \sin ^{2} \frac{3 \pi}{2 n+1}, \ldots, \sin ^{2} \frac{n \pi}{2 n+1}$;

b) $\operatorname{ctg}^{2} \frac{\pi}{2 n+1}, \operatorname{ctg}^{2} \frac{2 \pi}{2 n+1}, \operatorname{ctg}^{2} \frac{3 \pi}{2 n+1}, \ldots, \operatorname{ctg}^{2} \frac{n \pi}{2 n+1}$.

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