
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 triangle $ABC$ is inscribed in a circle. The measure of the non-overlapping minor arcs $AB$, $BC$, and $CA$ are, respectively, $x+50^\circ$, $2x+30^\circ$, and $4x-20^\circ$. Calculate the angle at vertex $A$ of the triangle.
A) $\frac{400}{7}^\circ$
B) $\frac{405}{7}^\circ$
C) $\frac{410}{7}^\circ$
D) $\frac{420}{7}^\circ$

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