
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 \(\sum_{i=1}^{n} x_{i} \leq \frac{1}{2}\), find the minimum value of \(f(x_{1}, x_{2}, \cdots, x_{n}) = \prod_{i=1}^{n} (1 - x_{i})\).

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