
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 the parabola $E: x^{2}=4y$ and the circle $F: x^{2}+\left(y-1\right)^{2}=1$, a line $l$ passing through point $F$ intersects the above two curves from left to right at points $A$, $C$, $D$, $B$ respectively. Find the minimum value of $|AC|+2|BD|$.

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