
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

A large piece of canvas is in the shape of an isosceles triangle with \( AC = BC = 5 \) m and \( AB = 6 \) m. Point \( D \) is the midpoint of \( AB \).

The canvas is folded along median \( CD \) to create two faces of a tent \((\triangle ADC \) and \(\triangle BDC)\). The third face of the tent \((\triangle ABD)\) is made from a separate piece of canvas. The bottom of the tent \((\triangle ABC)\) is open to the ground.

What is the height of the tent (the distance from \( D \) to the base of \( \triangle ABC \)) when the volume of the tent is as large as possible?

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