
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
For all integers \( n \), \( F_{n} \) is defined by \( F_{n} = F_{n-1} + F_{n-2} \), with initial conditions \( F_{0} = 0 \) and \( F_{1} = 1 \). If \( a = F_{-5} + F_{-4} + \ldots + F_{4} + F_{5} \), find the value of \( a \).

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