
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 parametric equation of line \( l \) as \( \begin{cases} x=a-2ty \\ y=-4t \end{cases} \) (where \( t \) is the parameter), and the parametric equation of circle \( C \) as \( \begin{cases} x=4\cos \theta \\ y=4\sin \theta \end{cases} \) (where \( \theta \) is the parameter).  
(1) Find the standard equation of line \( l \) and circle \( C \).  
(2) If line \( l \) and circle \( C \) intersect, determine the range of the real number \( a \).

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