
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 the prime numbers \( p \) and \( q \) satisfying \( p q + p^{2} + q^{2} = 199 \) where \( p < q \), find the value of the algebraic expression \(\frac{2}{p(p+1)}+\frac{2}{(p+1)(p+2)}+\cdots+\frac{2}{(q-1) q} \).

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