
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
The function f(x) = [x] represents the largest integer not greater than x. For example, [-3.5] = -4, [2.1] = 2. A function g(x) = [x] + [2x] is defined on R. If A = {y | y = g(x), 0 ≤ x ≤ 1}, calculate the sum of all the elements in set A.

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