
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 triangle $ABC$ with side lengths $AB = 21$, $BC = 45$, and $AC = 36$, and points $G$ and $H$ on $AB$ and $AC$ respectively, with $AG = 15$ and $AH = 24$, calculate the ratio of the area of triangle $AGH$ to the area of quadrilateral $BCHG$.

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