
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 the only solution to the equation

$$
\pi / 4 = \operatorname{arcctg} 2 + \operatorname{arcctg} 5 + \operatorname{arcctg} 13 + \operatorname{arcctg} 34 + \operatorname{arcctg} 89 + \operatorname{arcctg}(x / 14)
$$

is a natural number. Find it.

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