
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 geometric sequence $\{a\_n\}$ satisfying $a\_n > 0$, $n=1$, $2$, $...$, and $a\_5 \cdot a\_{2n-5} = 2^{2n}$ ($n \geqslant 3$), find the value of $\log \_{2}a\_{1}+\log \_{2}a\_{3}+...+\log \_{2}a\_{2n-1}$ when $n \geqslant 1$.

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