
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 \(BC\) of the right triangle \(ABC\), a circle is constructed with \(BC\) as its diameter, which intersects the hypotenuse \(AB\) at point \(K\). Find the area of triangle \(CKB\) if leg \(BC\) is equal to \(a\) and leg \(AC\) is equal to \(b\).

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