
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 $x_{1}, x_{2}, \cdots, x_{n}$ satisfying the inequality $x_{1} + x_{2} + \cdots + x_{n} \leqslant \frac{1}{2}$, find the minimum value of $f\left(x_{1}, x_{2}, \cdots, x_{n}\right) = \prod_{i=1}^{n}\left(1 - x_{i}\right)$.

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