
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 $(xO)(y)$, a polar coordinate system is established with $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The polar coordinate equations of circle $C(_1)$ and line $C(_2)$ are $ρ = 4 \sin θ$ and $ρ \cos (θ - \frac{π}{4}) = 2 \sqrt{2}$, respectively.
1. Find the polar coordinates of the intersection points of $C(_1)$ and $C(_2)$;
2. Let $P$ be the center of circle $C(_1)$, and $Q$ be the midpoint of the line segment connecting the intersection points of $C(_1)$ and $C(_2)$. Given that the parametric equations of line $PQ$ are $\begin{cases} x = t^3 + a \\ y = \frac{b}{2} t^3 + 1 \end{cases}$ ($t \in \mathbb{R}$ is the parameter), find the values of $a$ and $b$.

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