
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 the positive semi-axis of the $x$-axis in the rectangular coordinate system as the polar axis, the polar coordinate equation of circle $M$ is $ρ = 2 \sin θ$, and the polar coordinate equation of line $l$ is $ρ \sin (θ + \frac{π}{4}) = \sqrt{2}$.
1. Write the rectangular coordinate equations of circle $M$ and line $l$.
2. Let $A$ and $B$ be the two intersection points of line $l$ and circle $M$. Find the value of $\frac{1}{PA} + \frac{1}{PB}$.

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