
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) = x² - ax + 2lnx,

1. Find the monotonic intervals of f(x) when a = 5.
2. If f(x) has two extreme points x₁ and x₂, and 1/3 < x₁ < 1/e < x₂, find the range of f(x₁) - f(x₂). (Where e is the base of the natural logarithm)

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