
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 by $a_1 = 2$, $a_2 = \frac{5}{11}$, and the recursive relationship 
\[a_n = \frac{3a_{n-2} \cdot a_{n-1}}{4a_{n-2} - a_{n-1}}\] for $n \geq 3$. Find $a_{2023}$ written in simplest form as $\frac{p}{q}$, where $p$ and $q$ are coprime. What is $p+q$?
A) 8078
B) 8092
C) 8117
D) 8131

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