
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 a polar coordinate system where the pole is the origin of the Cartesian coordinate system, the polar axis is the positive half of the $x$-axis, and the unit length is the same, consider the curves $C_1: \rho =1$ and $C_2: \begin{cases} & x=\frac{\sqrt{2}}{2}t-1 \\ & y=\frac{\sqrt{2}}{2}t+1 \end{cases}$ (where $t$ is a parameter).

(Ⅰ) Find the minimum distance from a point on curve $C_1$ to the line $C_2$;

(Ⅱ) If we expand the $x$-coordinates of the points on $C_1$ to twice their original size and the $y$-coordinates to $\sqrt{3}$ times their original size, we obtain the curve $C_1'$. Let $P(-1,1)$, and the curve $C_2$ intersects with $C_1'$ at points $A$ and $B$. Find $|PA|+|PB|$.

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