
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 \( a, b, n \in \mathbf{R}_{+} \), find the minimum value of \( y = \frac{a}{\sqrt{(1+x)^{n}}} + \frac{b}{\sqrt{(1-x)^{n}}} \) for \( x \in (-1, 1) \).

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