
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]


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In the quadrilateral $ABCD$ with point $E$ inside it, angles at $E$ formed by lines from $E$ to each vertex are $a, b, c, d$. Given that $AE$ bisects $\angle BAC$ in $\triangle ABC$, solve for $d$ in terms of $a, b$, and $c$ where $\angle BAC = s$.
**A)** $360^\circ - \left(\frac{s}{2} + b + c\right)$

**B)** $360^\circ - \left(s + b + c\right)$

**C)** $\frac{s}{2} + b + c$

**D)** $\frac{360^\circ - (b + c)}{2}$

**E)** $\frac{s + b + c}{2}$

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