
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 sequence of positive integers is given by \( a_{1} = 1 \) and \( a_{n} = \operatorname{gcd} \left( a_{n-1}, n \right) + 1 \) for \( n > 1 \). Calculate \( a_{2002} \).

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