
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 non-negative real numbers \( x_{1}, x_{2}, \cdots, x_{n} \) that satisfy the inequality
\[ x_{1} + x_{2} + \cdots + x_{n} \leq \frac{1}{2}, \]
find the minimum value of \( \left(1-x_{1}\right)\left(1-x_{2}\right) \cdots \left(1-x_{n}\right) \).

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