
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
The minimum value of the function \( f(x) = (\sqrt{1+x} + \sqrt{1-x} - 3)\left(\sqrt{1-x^2} + 1\right) \) is \( m \), and the maximum value is \( M \). Then \( \frac{M}{m} = \) .

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