
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, y_1) and P_2(x_2, y_2) are two points on a unit circle with center at the origin O, and ∠P_1OP_2 = θ (θ is an obtuse angle). If sin(θ + π/4) = 3/5, find the value of x_1x_2 + y_1y_2.

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