
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 xy-plane of the Cartesian coordinate system, point P($x_0$, $y_0$) lies on the unit circle O. Let ∠xOP = α, where $$α ∈ (\frac{π}{4}, \frac{3π}{4})$$. If $$cos(α + \frac{π}{4}) = -\frac{12}{13}$$, find the value of $x_0$.

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