
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 $DC = 9$, $CB = 7$, $AB = \frac{1}{3}AD$, and $ED = \frac{2}{3}AD$, find $FC$. Express your answer as a decimal.  
[asy]
draw((0,0)--(-24,0)--(-24,18)--cycle);
draw((-15,0)--(-15,12));
draw((-6,0)--(-6,6));
draw((-6,0.5)--(-6+0.5,0.5)--(-6+0.5,0));
draw((-15,0.5)--(-15+0.5,0.5)--(-15+0.5,0));
draw((-24,0.5)--(-24+0.5,0.5)--(-24+0.5,0));
label("A",(0,0),E);
label("B",(-6,0),S);
label("G",(-6,6),N);
label("C",(-15,0),S);
label("F",(-15,12),N);
label("D",(-24,0),S);
label("E",(-24,18),N);
[/asy]

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