
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
A sequence of numbers is defined recursively by $b_1 = 2$, $b_2 = \frac{5}{11}$, and
\[b_n = \frac{b_{n-2} \cdot b_{n-1}}{3b_{n-2} - 2b_{n-1}}\] for all $n \geq 3$. Calculate $b_{10}$ and express it as $\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. What is $p+q$?
A) 4
B) 5
C) 6
D) 7

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