
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
Points  $P$  and  $Q$  are chosen on diagonal  $AC$  of square  $ABCD$  such that  $AB=AP=CQ=1$ . What is the measure of  $\angle{PBQ}$  in degrees?

*2019 CCA Math Bonanza Lightning Round #1.3*

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