
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) = e^x - $\frac{1}{2}$ax^2 - b.
1. When a = 1 and b = 1, find the range of f(x) on the interval [-1, 1].
2. If f(x) ≥ 0 holds true for any real number x, find the maximum value of a + b.

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