
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
From a point $A$ outside a circle, two tangents are drawn to the circle, touching the circle at points $B$ and $C$. The circle is then rotated such that the arcs divided by points $B$ and $C$ have lengths in the ratio of $3:4$. Find the degree measure of $\angle{BAC}$.
- **A** $\frac{480}{7}^\circ$
- **B** $\frac{510}{7}^\circ$
- **C** $\frac{540}{7}^\circ$
- **D** $\frac{570}{7}^\circ$
- **E** $\frac{600}{7}^\circ$

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