
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
Two tangents, $l_1$ and $l_2$, are drawn to the parabola $y = x^2$ at points $A\left(1, y_1\right)$ and $B\left(x_2, y_2\right)$ respectively. The tangents $l_1$ and $l_2$ intersect at point $C$. If the dot product $\overrightarrow{AC} \cdot \overrightarrow{BC} = 0$, determine the value of $x_2$.

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