
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 \( a_1 = 2 \), \( a_2 = \frac{5}{3} \), and for all \( n \geq 3 \),
\[
a_n = \frac{3a_{n-2} \cdot a_{n-1}}{4a_{n-2} - 2a_{n-1}}
\]
Find \( a_5 \) and express it as a fraction \( \frac{p}{q} \) where \( p \) and \( q \) are relatively prime positive integers. What is \( p+q \)?
A) 210
B) 212
C) 213
D) 214
E) 215

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