
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
In the polar coordinate system, the polar coordinate equation of curve $C\_1$ is $ρ(sin⁡θ+cos⁡θ)=1$, and the polar coordinate equation of curve $C\_2$ is $ρ=2cos⁡θ-4sin⁡θ$,
(1) Curve $C\_1$ intersects curve $C\_2$ at two points $A$ and $B$. Find the distance between points $A$ and $B$;
(2) Let point $M(x, y)$ be any point on curve $C\_2$ in the rectangular coordinate system. Find the maximum value of $x + y$.

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