
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
Let \( a_{0} = 2 \) and for \( n \geq 1 \), \[ a_{n} = \frac{\sqrt{3} a_{n-1} + 1}{\sqrt{3} - a_{n-1}}. \] Find the value of \( a_{2002} \) in the form \( p + q \sqrt{3} \) where \( p \) and \( q \) are rational numbers.

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