
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  $\angle ABC = \angle BCD = 90^o$ ,  $AB = 3$ ,  $BC = 6$ , 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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