
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 sequence $\{a\_n\}$ is a positive geometric sequence satisfying $\log \_{2}a\_{n+1}=1+\log \_{2}a\_{n}\ (n\in\mathbb{N^*})$, and $a\_{1}+a\_{2}+a\_{3}+a\_{4}+a\_{5}=2$, find the common ratio $q=$____; and $\log \_{2}(a\_{51}+a\_{52}+a\_{53}+a\_{54}+a\_{55})=$____.

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