
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 that $x_1 \cdot x_2 \cdot \ldots \cdot x_{2008} = 1$, and $x_1, x_2, \ldots, x_{2008}$ are all positive numbers, find the minimum value of $(1+x_1)(1+x_2)\ldots(1+x_{2008})$.

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