
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 vectors \(\boldsymbol{a} = (1, x)\) and \(\boldsymbol{b} = \left(x^2 + x, -x\right)\), where \(m\) is a constant and \(m \leq -2\), find the range of \(x\) such that \(\boldsymbol{a} \cdot \boldsymbol{b} + 2 > m \left( \frac{2}{\boldsymbol{a} \cdot \boldsymbol{b}} + 1 \right)\) holds.

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