
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
A finite sequence $a_1, a_2, a_3, \ldots, a_m$ (where $m$ is a positive integer) is said to be "symmetrical" if it meets the conditions $a_1 = a_m$, $a_2 = a_{m-1}$, ..., $a_m = a_1$, i.e., $a_i = a_{m-i+1}$ for $i = 1, 2, \ldots, m$. For example, the sequences $1, 2, 5, 2, 1$ and $8, 4, 2, 2, 4, 8$ are both "symmetrical". Consider a sequence $\{b_n\}$ of 7 terms that is "symmetrical", where $b_1, b_2, b_3, b_4$ form a geometric sequence, and $b_1 = 2$, $b_3 = 8$. Find the sum of all terms in the sequence $\{b_n\}$.

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