
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 "hinged" kite has sides of length $3 \text{ cm}$ and $4 \text{ cm}$, and its angles can be varied. What are the lengths of the diagonals of the convex kite if its area is half of the maximum possible area?

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