
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 parameterized equations of curve $C\_1$ in the rectangular coordinate system are $x=\frac{\sqrt{5}}{5}t$ and $y=\frac{2\sqrt{5}}{5}t-1$, where $t$ is the parameter. With the origin $O$ as the pole and the non-negative part of the $x$-axis as the polar axis, establish a polar coordinate system. There is another curve $C\_2$: $ρ=2\cos⁡θ−4\sin⁡θ$.

(1) Convert the equations of $C\_1$ to a standard form and find the rectangular coordinate equation of $C\_2$.

(2) Calculate the distance between the intersection points of curves $C\_1$ and $C\_2$.

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