
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 that $P_{1}(x_{1},x_{2})$ and $P_{2}(x_{2},y_{2})$ are two points on a unit circle with center at the origin $O$, and $\angle P_{1}OP_{2}=\theta$ ($\theta$ is an obtuse angle). If $\sin (\theta+ \frac {π}{4})= \frac {3}{5}$, find the value of $x_{1}x_{2}+y_{1}y_{2}$.

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