
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
Distinct points $P$, $Q$, $R$, $S$ lie on the circle $x^{2}+y^{2}=169$ and have integer coordinates. The sum of distances $PQ + RS$ is an irrational number. What is the greatest possible value of the ratio $\frac{PQ}{RS}$?
A) 2
B) 3
C) 2.5
D) 2.4

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