
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
Alexandra draws a letter A which stands on the $x$-axis.

(a) The left side of the letter A lies along the line with equation $y=3x+6$. What is the $x$-intercept of the line with equation $y=3x+6$?

(b) The right side of the letter A lies along the line $L_{2}$ and the letter is symmetric about the $y$-axis. What is the equation of line $L_{2}$?

(c) Determine the area of the triangle formed by the $x$-axis and the left and right sides of the letter A.

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