
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
Calculate the following integrals:
\[ \int \frac{d x}{x\left(1+\ln ^{2} x\right)}, \quad \int \frac{e^{x} d x}{1+e^{2 x}}, \quad \int \frac{\cos x d x}{1+\sin ^{2} x}. \]

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