
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) How can we select some number of vectors from $\overline{O A}_{1}, \overline{O A}_{2}, \overline{O A}_{3}, \ldots, \overline{O A}_{25}$, where $O$ is the center of a regular 25-sided polygon $A_{1} A_{2} A_{3} \ldots A_{25}$, so that the length of the sum of these vectors is as large as possible?

b) What is this length if all the vectors considered are unit vectors?

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