
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 the right triangle \(ABC\), a circle is constructed with \(AC\) as its diameter, intersecting the hypotenuse \(AB\) at point \(K\).

Find \(CK\) if \(AC = 2\) and \(\angle A = 30^\circ\).

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