
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
Let \(ABCD\) be a rhombus where \(AB=10\), \(AC=16\), and \(\angle ABC = 60^\circ\). Extend \(\overline{CD}\) through \(D\) to \(E\) so that \(DE=6\). If \(\overline{BE}\) intersects \(\overline{AD}\) at \(F\), determine the length of \(FD\).
A) 3.6
B) 3.7
C) 3.75
D) 3.8
E) 3.9

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