
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 \( \triangle ABC \), \( \angle ABC = 150^\circ \), \( AB = 5 \) and \( BC = 7 \). Perpendiculars are constructed to \( \overline{AB} \) at \( A \) and to \( \overline{BC} \) at \( C \) that meet at point \( D \). Find the length of \( CD \).

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