
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^x (a > 0, a ≠ 1).
(I) If $f(1) + f(-1) = \frac{5}{2}$, find the value of f(2) + f(-2).
(II) If the difference between the maximum and minimum values of the function f(x) on [-1, 1] is $\frac{8}{3}$, find the value of the real number a.

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