
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 the rhombus \(ABCD\), a height \(DE\) is dropped on side \(BC\). The diagonal \(AC\) of the rhombus intersects the height \(DE\) at point \(F\), where \(DF : FE = 5\).

Find the side length of the rhombus, given that \(AE = 5\).

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