
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 derivative of the function \( u = \sqrt{x^2 + y^2} \) at the point \( A(3, 4) \):
1) in the direction of the bisector of the first coordinate angle,
2) in the direction of the radius vector of point \( A \),
3) in the direction of the vector \( \mathbf{q} \{4, -3\} \).

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