
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 an inscribed quadrilateral \(ABCD\), the degree measures of the angles are in the ratio \(\angle A : \angle B : \angle C = 2 : 3 : 4\). Find the length of \(AC\), given that \(CD = 21\) and \(BC = 14\sqrt{3} - 10.5\).

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