
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 triangle \(ABC\), angle \(C\) is a right angle. From center \(C\), an arc with radius \(AC\) is drawn, intersecting the hypotenuse at point \(D\) and the leg \(CB\) at point \(E\). 

Find the angular measures of arcs \(AD\) and \(DE\), given that \(\angle B = 40^\circ\).

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