
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
For what value of \( x \) is the fourth term in the expansion of \( \left(\sqrt{2^{x-1}}+\sqrt[3]{2^{-x}}\right)^{m} \) 20 times greater than \( m \), if the binomial coefficient of the fourth term is related to the binomial coefficient of the second term as 5:1?

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