
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_n} be a sequence of positive numbers with the sum of its first n terms being b_n. Let {b_n} be such that the product of its first n terms is c_n, and b_n + c_n = 1. The number in the sequence {1/a_n} that is closest to 2002 is ___ .

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