
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 an ellipse $C: \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 \left( a > b > 0 \right)$ with eccentricity $\dfrac{\sqrt{3}}{2}$, and the length of its minor axis is $2$.

(I) Find the standard equation of the ellipse $C$.

(II) Suppose a tangent line $l$ of the circle $O: x^2 + y^2 = 1$ intersects curve $C$ at points $A$ and $B$. The midpoint of segment $AB$ is $M$. Find the maximum value of $|OM|$.

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