
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 diagram below, the point \( D \) lies inside the triangle \( ABC \) such that \(\angle BAD = \angle BCD\) and \(\angle BDC = 90^\circ\). Given that \( AB = 5 \) and \( BC = 6 \), and the point \( M \) is the midpoint of \( AC \), find the value of \( 8 \times DM^2 \).

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