
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
Point P is on the parabola y^{2}=4x. Let d_{1} be the distance from P to the directrix of the parabola, and d_{2} be the distance from P to the line x-2y+10=0. Determine the minimum value of d_{1}+d_{2}.

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