
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 that the focus of the parabola $y^2=4x$ is F, and the points M($\frac{1}{4}$, a), N($\frac{1}{2}$, b), P(1, c), and Q(4, d) are all on the parabola. Determine the point among M, N, P, and Q that has the minimum distance to the focus F.

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