
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 $DC = 5$, $CB = 9$, $AB = \frac{1}{3}AD$, and $ED = \frac{2}{3}AD$, find $FC$. [asy]
draw((0,0)--(-20,0)--(-20,16)--cycle);
draw((-12,0)--(-12,10.4));
draw((-5,0)--(-5,4));
draw((-5,0.5)--(-5+0.5,0.5)--(-5+0.5,0));
draw((-12,0.5)--(-12+0.5,0.5)--(-12+0.5,0));
draw((-20,0.5)--(-20+0.5,0.5)--(-20+0.5,0));
label("A",(0,0),E);
label("B",(-5,0),S);
label("G",(-5,4),N);
label("C",(-12,0),S);
label("F",(-12,10.4),N);
label("D",(-20,0),S);
label("E",(-20,16),N);
[/asy]

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