
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) = x + a(e^(2x) - 3e^x + 2), where a ∈ R:
1. Discuss the number of extreme points of the function f(x) and explain the reasons.
2. If ∀x > 0, f(x) ≥ 0 holds, find the range of a.

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