
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
Line $l$: $\left\{{\begin{array}{l}{x=a-2t,}\\{y=-1+t}\end{array}}\right.$ (where $t$ is a parameter, $a\neq 0$), circle $C$: $ρ=2\sqrt{2}\cos({θ+\frac{π}{4}})$ (the polar axis coincides with the non-negative x-axis, and the unit length is the same). <br/>$(1)$ Find the distance from the center of circle $C$ to line $l$;<br/>$(2)$ If the chord cut by line $l$ on circle $C$ has a length of $\frac{{6\sqrt{5}}}{5}$, find the value of $a$.

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