
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 $\triangle ABC$, the incircle is denoted as $\odot O$. A line is drawn through $O$ parallel to $BC$ and intersects $AB$ and $AC$ at points $D$ and $E$ respectively. Given that the lengths of the sides $BC$, $CA$, and $AB$ of $\triangle ABC$ are 8, 7, and 5 respectively, find the length of $DE$.

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