
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 the function $f(x) = a\ln x + (x + 1)^2$ $(x > 0)$, for any two distinct points $P(x_1, y_1)$ and $Q(x_2, y_2)$ on the graph of $f(x)$, it always holds that $f(x_1) - f(x_2) \geqslant 4(x_1 - x_2)$. Find the range of the real number $a$.

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