
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 point \( A(3,1) \) and point \( F \) as the focus of the parabola \( y^{2}=5x \), let \( M \) be a variable point on the parabola. When \( |MA| + |MF| \) takes its minimum value, the coordinates of point \( M \) are _______.

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