
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 $f(x)=2^{x}$, the common difference of the arithmetic sequence $\{a\_n\}$ is $2$. If $f(a\_2+a\_4+a\_6+a\_8+a\_10)=4$, then $\log\_2[f(a\_1)⋅f(a\_2)⋅f(a\_3)⋅…⋅f(a\_10)]=$ \_\_\_\_\_\_ .

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