
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 the sequence {a<sub>n</sub>} with the sum of the first n terms S<sub>n</sub>, and S<sub>n</sub> - a<sub>n</sub> = (n-1)<sup>2</sup>, b<sub>n</sub> = $\frac{{2^{{a_n}}}}{{S_n^2}}$, find the term number of the minimum value in the sequence {b<sub>n</sub>}.

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