
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 the first differential of the function \( y(x) = \operatorname{arctg}\left(\frac{1}{x}\right) \) and compute its value at \( x = 1 \) given \( dx = \Delta x = -0.1 \).

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