
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 points $A$ and $B$ on a unit circle $O$, and point $P$ on the plane of the unit circle $O$ such that $\overrightarrow{OA}$ and $\overrightarrow{OB}$ are not collinear.

(1) In $\triangle OAB$, point $P$ is on $AB$ and $\overrightarrow{AP} = 2\overrightarrow{PB}$. If $\overrightarrow{AP} = r\overrightarrow{OB} + s\overrightarrow{OA}$, find the value of $r + s$.

(2) Given that point $P$ satisfies $\overrightarrow{OP} = m\overrightarrow{OA} + \overrightarrow{OB}$ (where $m$ is a constant), and $OABP$ is a parallelogram, find the value of $m$.

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