
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
Let JOHN be a rhombus with JH = 16 and ON = 12. Let G and P be points in JN and HN respectively such that JG: GN: NP = 2: 2: 1. What is the length GP? 

(a) \(\frac{2 \sqrt{19}}{5}\) \\
(b) \(\frac{2 \sqrt{13}}{3}\) \\
(c) \(\frac{3 \sqrt{17}}{2}\) \\
(d) \(\frac{3 \sqrt{15}}{2}\)

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