
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]


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In the convex quadrilateral \(ABCD\), \(E\) is the intersection of the diagonals. The areas of triangles \(ADE, BCE, CDE\) are \(12 \, \text{cm}^2, 45 \, \text{cm}^2, 18 \, \text{cm}^2\), respectively, and the length of side \(AB\) is \(7 \, \text{cm}\).

Determine the distance from point \(D\) to the line \(AB\).

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