
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
Find all values of \(x\) for which the expressions

$$
\log_{2011}\left(\sqrt{1+\operatorname{ctg}^{2} x}+\operatorname{ctg} x\right) \quad \text{and} \quad \log_{2013}\left(\sqrt{1+\operatorname{ctg}^{2} x}-\operatorname{ctg} x\right)
$$

are equal to each other.

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