
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 with pole $O$, the curve $C\_1$: $ρ=2$ intersects with the curve $C\_2$: $ρ\sin \left( θ-\frac{π}{4} \right)=\sqrt{2}$ at two distinct points $A$, $B$.

(1) Find the value of $|AB|$;

(2) Find the polar coordinate equation of the line $l$ that passes through point $C(1,0)$ and is parallel to line $AB$.

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