
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 a configuration where two triangles $\triangle ABC$ and $\triangle DEF$ are such that $\angle BAC = \angle DEF$, the sides of triangle $\triangle ABC$ are given by $AB = 5.1$, $AC = 5.1$. If the side $DE = 1.7$, find the length of side $DF$ such that the areas of $\triangle ABC$ and $\triangle DEF$ are equal.
A) 15.3
B) 10.2
C) 20.4
D) 25.5

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