
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 an arithmetic sequence $\{a\_n\}$ with the sum of the first $n$ terms denoted as $S\_n$, and $S\_4 = a\_5 - a\_1$.

1. Find the common ratio $q$ of the sequence $\{a\_n\}$.
2. Let $b\_n = \log\_2{a_{n+1}}$. The sum of the first $n$ terms of the sequence $\{b\_n\}$ is denoted as $T\_n$. If $T\_4 = 2b\_5$, find the value of $a\_1$.

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