
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 triangle $DEF$, $DE=135$, $DF=143$, and $EF=132$. The angle bisector of angle $D$ intersects $\overline{EF}$ at point $S$, and the angle bisector of angle $E$ intersects $\overline{DF}$ at point $R$. Let $U$ and $V$ be the feet of the perpendiculars from $F$ to $\overline{ER}$ and $\overline{DS}$, respectively. Find $UV$.

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