
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
What is the maximum rate at which the function \( u(M) = \frac{10}{x^2 + y^2 + z^2 + 1} \) can increase as the point \( M(x, y, z) \) passes through the point \( M_0(-1, 2, -2) \)? In which direction should the point \( M \) move as it passes through the point \( M_1(2, 0, 1) \) for the function \( u(M) \) to decrease at the greatest rate?

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