
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  $ABC$  be a triangle inscribed in the parabola  $y=x^2$  such that the line  $AB \parallel$  the axis  $Ox$ . Also point  $C$  is closer to the axis  $Ox$  than the line  $AB$ . Given that the length of the segment  $AB$  is 1 shorter than the length of the altitude  $CH$  (of the triangle  $ABC$ ). Determine the angle  $\angle{ACB}$  .

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