
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
It is known that  $\int_1^2x^{-1}\arctan (1+x)\ dx = q\pi\ln(2)$  for some rational number  $q.$  Determine  $q.$  Here,  $0\leq\arctan(x)<\frac{\pi}{2}$  for  $0\leq x <\infty.$ 

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