
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 a geometric sequence $\{a_n\}$ with a common ratio not equal to 1 that satisfies $\log_{2}(a_1 \cdot a_2 \cdots a_{13}) = 13$, and an arithmetic sequence $\{b_n\}$ that satisfies $b_7 = a_7$, find the value of $b_1 + b_2 + \cdots + b_{13}$.

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