
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
In the parallelogram $ABCD$, let $H$ be the point that trisects the side $AB$ closer to $A$, $F$ be the midpoint of the side $BC$, and $G$ be the point that quarters the side $DA$ closer to $A$. In what ratio does the segment $HC$ divide the segment $FG$?

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