
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 \( a_n \) recursively where \( a_1 = 4 \), \( a_2 = \frac{8}{3} \), and for \( n \geq 3 \),
\[ a_n = \frac{a_{n-1} \cdot a_{n-2}}{3a_{n-2} - 2a_{n-1}}. \]
Find \( a_6 \) expressed as a fraction \( \frac{p}{q} \) where \( p \) and \( q \) are relatively prime positive integers. What is \( p+q \)?
- **A)** 11
- **B)** 12
- **C)** 13
- **D)** 14
- **E)** 15

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