
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
In the Cartesian coordinate system $xOy$, there is a fixed point $C(0,-4)$. $P$ is a moving point on the circle $(x-2)^{2}+(y-4)^{2}=1$, and $M$ is the midpoint of $PC$. Point $B$ is on the parabola $y^{2}=4x$. The maximum value of $\dfrac{|BO|}{|BM|}$ is ______.

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