
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 diagram, $\triangle ABF$, $\triangle BCF$, and $\triangle CDF$ are right-angled, with $\angle ABF=\angle BCF = 60^\circ$, and $\angle CDF = 45^\circ$, and $AF=48$. [asy]
pair A, B, C, D, F;
A=(0,41.57);
B=(0,0);
C=(18,-10.392);
D=(27,-5.196);
F=(24,0);
draw(A--B--C--D--F--A);
draw(B--F);
draw(C--F);
label("A", A, N);
label("B", B, W);
label("C", C, SW);
label("D", D, dir(0));
label("F", F, NE);
[/asy] Find the length of $CF.$

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