
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
The diagonal \( AC \) of parallelogram \( ABCD \) is three times longer than the diagonal \( BD \) and intersects it at an angle of \( 60^{\circ} \). Find the length of the segment connecting vertex \( D \) with the midpoint of side \( BC \), given that \( AC = 24 \) and angle \( BDC \) is obtuse.

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