
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

a) The difference between two consecutive but not adjacent angles is $100^{\circ}$. Determine the angle formed by their bisectors.

b) In the drawing below, $D A$ is the bisector of angle $\angle C A B$. Determine the value of angle $\angle D A E$ knowing that $\angle C A B + \angle E A B = 120^{\circ}$ and $\angle C A B - \angle E A B = 80^{\circ}$.

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