
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]


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In an arithmetic sequence with 2013 terms, denoted as $\{a_n\}$, the equation $(a\_1+a\_3+...+a\_{2013})-(a\_2+a\_4+...+a\_{2012})=a\_{1007}$ holds true. Analogous to this property, find the corresponding equation in a geometric sequence with 2011 terms, denoted as $\{b_n\}$.

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