
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
Given a sequence of numbers defined recursively by \( b_1 = 2 \), \( b_2 = \frac{7}{2} \), and for \( n \geq 3 \),
\[
b_n=\frac{b_{n-2} \cdot b_{n-1}}{2b_{n-2} - b_{n-1}}
\]
determine the value of \( b_{2020} \) and express it as \( \frac{p}{q} \), where \( p \) and \( q \) are relatively prime positive integers, and calculate the sum \( p + q \).

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