
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 P<sub>1</sub>(x<sub>1</sub>, y<sub>1</sub>) and P<sub>2</sub>(x<sub>2</sub>, y<sub>2</sub>) on a unit circle with center O, and ∠P<sub>1</sub>OP<sub>2</sub>=θ (θ is an obtuse angle). If sin(θ + $\frac{π}{4}$) = $\frac{3}{5}$, find the value of x<sub>1</sub>x<sub>2</sub> + y<sub>1</sub>y<sub>2</sub>.

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