
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 $a_1 = 2$ and $a_2 = \frac{5}{11}$. The recursive relation for $n \geq 3$ is given by 
\[ a_n = \frac{2a_{n-2} \cdot a_{n-1}}{3a_{n-2} - a_{n-1}} \]
Find $a_{2023}$ expressed as $\frac{p}{q}$, where $p$ and $q$ are coprime integers. What is $p+q$?
A) 12145
B) 12148
C) 12150
D) 12152

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