
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 that the geometric sequence $\{a_n\}$ satisfies $a_n > 0$ for $n=1,2,\dots$, and $a_5 \cdot a_{2n-5} = 2^{2n}$ $(n \geq 3)$, determine the value of $\log_{2}a_1 + \log_{2}a_3 + \dots + \log_{2}a_{2n-1}$ for $n \geq 1$.

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