
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 a convex quadrilateral \(ABCD\), diagonal \(AC\) is drawn, \(AD = 7\), \(BC = 3\), and \(\angle ACD = 60^\circ\). It is known that points \(A\), \(B\), \(C\), and \(D\) lie on the same circle, and the perpendicular dropped from point \(A\) to side \(CD\) bisects \(\angle BAD\). Find the length of diagonal \(AC\).

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