
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 $l$ in the coordinate plane has equation $2x - 3y + 30 = 0$. This line is rotated $30^{\circ}$ counterclockwise about the point $(10,10)$ to obtain line $k$. What is the $x$-coordinate of the $x$-intercept of line $k?$
A) $20\sqrt{3} - 20$
B) $15\sqrt{3} - 15$
C) $10\sqrt{3} - 10$
D) $5\sqrt{3} - 5$
E) $25\sqrt{3} - 25$

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