
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 $\{a_n\}$ where $a_1 = 1$ and the sum of the first 10 terms $S_{10} = 100$:
1. Find the common difference $d$ of the sequence $\{a_n\}$.
2. Determine the general formula for the sequence $\{a_n\}$.
3. Let $b_n = 2^{a_n + 1}$. Determine whether $\{b_n\}$ is a geometric sequence, and explain the reasoning.

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