
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
Let \( ABCD \) be a convex trapezoid such that \(\angle ABC = \angle BCD = 90^\circ\), \( AB = 3 \), \( BC = 6 \), and \( CD = 12 \). Among all points \( X \) inside the trapezoid satisfying \(\angle XBC = \angle XDA\), compute the minimum possible value of \( CX \).

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