
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 sequence of numbers where $b_1 = 2$, $b_2 = \frac{5}{11}$, and for all $n \geq 3$,
\[b_n = \frac{b_{n-2} \cdot b_{n-1}}{3b_{n-2} - 2b_{n-1}}\]
Find $b_3$ in its simplest form, and sum the numerator and denominator of the simplified fraction.
A) $30$
B) $32$
C) $33$
D) $35$

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