
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 a Cartesian coordinate system with the origin as the pole and the positive x-axis as the polar axis, establish a polar coordinate system using the same unit length as the Cartesian one. Given the curve \( C \): \( \rho = a \) (where \( a > 0 \)), and the line \( l \) passing through point \( P(0, 2) \) with the parametric equation 
$$
\begin{cases}
x = \frac{t}{2} \\
y = 2 + \frac{\sqrt{3}}{2}t
\end{cases}
$$
(where \( t \) is the parameter),  
(I) find the standard equation of curve \( C \) and line \( l \);  
(II) suppose curve \( C \) undergoes a scaling transformation 
$$
\begin{cases}
x' = 2x \\
y' = y
\end{cases}
$$
to become curve \( C' \). If line \( l \) is tangent to curve \( C' \), find the value of the real number \( a \).

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