
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
Let $\{a_n\}$ be an arithmetic sequence with sum of the first n terms, S_n, given by $S_n$. Given that $S_9=-36$ and $S_{13}=-104$, find the value of $b_6$ in the geometric sequence $\{b_n\}$, where $b=a_5$ and $b_7=a_7$.

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