
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
On the graph of the function $f(x) = a\ln{x} + (x+1)^2$ ($x > 0$), take any two distinct points P($x_1, y_1$) and Q($x_2, y_2$). It is always possible to ensure that $f(x_1) - f(x_2) \geq 4(x_1 - x_2)$. What is the range of the real number $a$?

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