
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
A triangle  $ABC$  with orthocenter  $H$  is inscribed in a circle with center  $K$  and radius  $1$ , where the angles at  $B$  and  $C$  are non-obtuse. If the lines  $HK$  and  $BC$  meet at point  $S$  such that  $SK(SK -SH) = 1$ , compute the area of the concave quadrilateral  $ABHC$ .

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