
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 hypotenuse \(AB\) of the right triangle \(ABC\), a square \(ABDE\) is constructed on the side of the plane that does not include the triangle \(ABC\). Find the distance from the vertex \(C\) of the right angle of the triangle to the center of the square, given that \(BC = a\) and \(AC = b\).

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