
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
On the leg \(AC\) of a right triangle \(ABC\), a circle is constructed with \(AC\) as its diameter, intersecting the hypotenuse \(AB\) at point \(K\). Find the area of triangle \(CKB\), given that leg \(AC\) is equal to \(b\), and angle \(ABC\) is equal to \(\beta\).

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