
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 $a\_n = \int\_0^n (2x + 1)dx$, the sum of the first $n$ terms of the sequence ${\frac{1}{a\_n}}$ is $S\_n$, and the general term of the sequence ${b\_n}$ is $b\_n = n - 35$, $n \in \mathbb{N}^*$, determine the minimum value of $b\_n S\_n$.

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