
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
Let \( f(x) \) be a function defined on \( \mathbb{R} \). For any real number \( x \), it holds that \( f(x+3) \cdot f(x-4) = -1 \). Additionally, when \( 0 \leq x < 7 \), \( f(x) = \log_{2}(9-x) \). Determine the value of \( f(-100) \).

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