
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 rectangular coordinate system $(xOy)$, the curve $(C_1:\begin{cases}x=t\cos α, \\\\ y=t\sin α,\end{cases} (t\neq 0))$, where $0\leqslant α < π $. In the polar coordinate system with $O$ as the pole and the positive half of the $x$-axis as the polar axis, the curves $(C_2:ρ=2\sin θ )$ and $(C_3:ρ=2 \sqrt{3}\cos θ )$.

1. Find the rectangular coordinates of the intersection point(s) of $C_2$ and $C_3$;
2. If $C1$ intersects with $C2$ at point $A$, and $C1$ intersects with $C3$ at point $B$, find the maximum value of $|AB|$.

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