
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 parallelogram with sides $\overline{AB} = \overline{CD} = 15$ and $\overline{BC} = \overline{DA} = 20$. The diagonals are perpendicular with one of the diagonals, $\overline{AC}$, being $25$. Let $E$ be the midpoint of diagonal $\overline{BD}$, and let $F$ be a point on $\overline{CD}$ such that $DF = 5$. Find the length of $EF$.

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