
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 $\left\{\frac{1}{a_n}\right\}$ is $S_n$, and the general term of the sequence $\{b_n\}$ is $b_n = n - 35$ for $n \in \mathbb{N}^{*}$, find the minimum value of $b_nS_n$.

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