
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
Given  $(a_n)_{n\geq 1}$  be a sequence such that  $a_1=1$  and  $3a_{n+1}-3a_n=1$  for all  $n\geq 1$ , find the value of  $a_{2002}$.

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