
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 parametric equations of curve C<sub>1</sub> as follows:
$$
\begin{cases} 
x= \sqrt {2} \cos θ \\ 
y= \sqrt {2} \sin θ 
\end{cases} \quad (\text{where } θ \text{ is the parameter}),
$$
and a polar coordinate system is established with the origin as the pole and the non-negative half of the x-axis as the polar axis. The polar equation of curve C<sub>2</sub> is given by $\rho \cos θ - \rho \sin θ = 0 \ (\rho \ge 0, 0 \le θ < 2π)$:
(Ⅰ) Find the polar coordinates of the intersection points of curves C<sub>1</sub> and C<sub>2</sub>;
(Ⅱ) Assume the intersection points of curves C<sub>1</sub> and C<sub>2</sub> are A and B. On the line segment AB there are two points C and D, where $|AC| = |BD| = \frac{\sqrt{2}}{2}$. Let P be a point on curve C<sub>1</sub>. Find the maximum value of $|PC| + |PD|$.

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