
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 $l$: $\begin{cases} x=at \\ y=1-2t \end{cases}$ ($t$ is a parameter) and the circle $C$: $ρ=2 \sqrt {2}\cos (θ+ \dfrac {π}{4})$ (the polar axis coincides with the non-negative semi-axis of $x$, and the unit length is the same), if there are at least three points on the circle $C$ that are exactly $\dfrac { \sqrt {2}}{2}$ away from the line $l$, then the range of the real number $a$ is \_\_\_\_\_\_.

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