
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 line $l$: $\begin{cases}x=l\cos 60 ^{\circ} \\ y=-1+l\sin 60 ^{\circ}\end{cases}(l\text{ is a parameter})$ and the curve $C$: $\begin{cases}x=2at^{2} \\ y=2at\end{cases}(t\text{ is a parameter, real number }a\neq 0)$, find the range of real number $a$ such that the line and the curve intersect at two distinct points.

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