
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 that function f(x) is an odd function defined on R, when x≥0, f(x)= $$\frac {1}{2}$$ (|x-a²|+|x-2a²|-3a²). If ∀x∈R, f(x-1)≤f(x), determine the range of the real number a.

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