
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 a function $f(x) = 2^x$, and an arithmetic sequence $\{a_n\}$ with a common difference of 2. If $f(a_2 + a_4 + a_6 + a_8 + a_{10}) = 4$, then find $\log_2 [f(a_1) \cdot f(a_2) \cdot f(a_3) \cdot \ldots \cdot f(a_{10})]$.

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