
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 $\{a_n\}$ is an arithmetic sequence with $a_3 = 5$ and $a_9 = 17$, and the sum of the first $n$ terms of the sequence $\{b_n\}$ is $S_n = 3^n - 1$. If $1 + a_m = b_4$, find the positive integer value of $m$.
Options:
A) 29
B) 28
C) 27
D) 26

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