
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
Find all values of \( b \) such that the following two inequalities hold for any real numbers \( x \) and \( y \):
$$
\left\{
\begin{array}{l}
2 b \cdot \cos 2(x-y) + 8 b^{2} \cdot \cos (x-y) + 8 b^{2}(b+1) + 5 b < 0 \\
x^{2} + y^{2} + 1 > 2 b x + 2 y + b - b^{2}
\end{array}
\right.
$$

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