
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
Given \( x, y, z \in (-1, 1) \) and \( x y z = \frac{1}{36} \), find the minimum value of the function \( u = \frac{1}{1-x^{2}} + \frac{4}{4-y^{2}} + \frac{9}{9-z^{2}} \).

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