
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
In right triangle \(ABC\), the angle bisector of the right angle at \(C\), \(CL\), is drawn. From vertex \(A\) (\(\angle A > 45^{\circ}\)), a perpendicular \(AD\) is dropped onto \(CL\). Find the area of triangle \(ABC\) if \(AD = a\) and \(CL = b\).

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