
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
In a circle of center  $O$  and radius  $r$ , a triangle  $ABC$  of orthocenter  $H$  is inscribed. It is considered a triangle  $A'B'C'$  whose sides have by length the measurements of the segments  $AB, CH$  and  $2r$ . Determine the triangle  $ABC$  so that the area of the triangle  $A'B'C'$  is maximum.

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