
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
1. If the proposition "$\exists x \in \mathbb{R}, x^2 + 2x + m \leqslant 0$" is a false statement, then the range of real number $m$ is ______.  
2. If the line $ax + 4y - l = 0$ is perpendicular to $2x - 5y + 6 = 0$, then the value of $a$ is ______.  
3. If the tangent line at point $P_0$ on the curve $y = x^3 + x - 2$ is parallel to the line $y = 4x - 1$, then the coordinates of $P_0$ are ______.  
4. Given the function $f(x) = \ln x + x^2 f''(a)$, and $f(1) = -1$, then the real number $a$ equals ______.

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