
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 the function $y=f(x)$, for any two distinct real numbers $x_1$, $x_2$, it holds that $f(x_1+x_2)=f(x_1)\cdot f(x_2)$, and $f(0)\neq 0$. Evaluate the product $f(-2007)\times f(-2006)\times \ldots \times f(2006)\times f(2007)$.

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