
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 a parabola with equation x^2 = 4y and a line l: 2x + 4y + 5 = 0, find the shortest distance from point P on the parabola to line l. The options are:
A) $\frac{\sqrt{5}}{5}$
B) $\frac{2\sqrt{5}}{5}$
C) $\frac{4\sqrt{5}}{5}$
D) $\sqrt{5}$

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