
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 point P on the parabola $y^2=8x$, let $d_1$ be the distance from P to the directrix of this parabola, and $d_2$ be the distance from P to the line $4x+3y+8=0$. Find the minimum value of $d_1+d_2$.

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