
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 two arithmetic sequences $\{a\_n\}$ and $\{b\_n\}$ with the sum of their first $n$ terms being $S\_n$ and $T\_n$ respectively. If $\frac{S\_n}{T\_n} = \frac{7n + 1}{4n + 27}$ for all positive integers $n$, find the value of $\frac{a\_7}{b\_7}$.

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