
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
In the cartesian coordinate system $xOy$, it is known that the line $y = x + 2$ intersects the $x$-axis and $y$-axis at points $M$ and $N$, respectively. Point $P$ moves on the circle $(x - a)^2 + y^2 = 2$ ($a > 0$). If the angle $\angle MPN$ is always acute, then the range of the real number $a$ is $\boxed{a > \sqrt{7} - 1}$.

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