
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 geometric sequence $\{a_n\}$ satisfying $a_n > 0$ for $n=1, 2, \ldots$, and $a_5 \cdot a_{2n-5} = 2^{2n}$ for $n \geqslant 3$, calculate the value of $\log_2 a_1 + \log_2 a_3 + \ldots + \log_2 a_{2n-1}$.

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