
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
Line $\ell$ in the coordinate plane has the equation $4x - 3y + 60 = 0$. This line is rotated $30^\circ$ counterclockwise around the point $(10, 10)$. What is the $x$-coordinate of the $x$-intercept of the resulting line $k$?
A) 7.0  
B) 7.5  
C) 8.5  
D) 9.0  
E) 9.5

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