
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
Define a new sequence \( (b_n) \) such that \( b_1 = 1 \), \( b_2 = \frac{1}{3} \), and for all \( n \geq 3 \),
\[ b_n = \frac{2 - b_{n-1}}{3b_{n-2} + 1}. \]
Find the value of \( b_{100} \).

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