
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
Given the parabola $y = -2x^2 + 4x + m$.
1. For what value of $m$ does the parabola intersect the x-axis at exactly one point?
2. If two points $A(x_1, y_1)$ and $B(x_2, y_2)$ on the parabola have $x$-coordinates satisfying $x_1 > x_2 > 2$, compare the values of $y_1$ and $y_2$.

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