
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 parabolic equation $y^2 = 8x$, and the equation of line $l$ is $x - y + 2 = 0$, find the minimum value of the sum of the distance from a point P on the parabola to the y-axis and the distance from P to the line $l$.

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