
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
Given acute triangle  $\triangle ABC$  in plane  $P$ , a point  $Q$  in space is defined such that  $\angle AQB = \angle BQC = \angle CQA = 90^\circ.$   Point  $X$  is the point in plane  $P$  such that  $QX$  is perpendicular to plane  $P$ . Given  $\angle ABC = 40^\circ$  and  $\angle ACB = 75^\circ,$  find  $\angle AXC.$ 

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