
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 \( n \) be the answer to this problem. In acute triangle \( ABC \), point \( D \) is located on side \( BC \) so that \(\angle BAD = \angle DAC\), and point \( E \) is located on \( AC \) so that \( BE \perp AC \). Segments \( BE \) and \( AD \) intersect at \( X \) such that \(\angle BXD = n^{\circ}\). Given that \(\angle XBA = 16^{\circ}\), find the measure of \(\angle BCA\).

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