
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
If $d$ represents the length of the solution interval for the inequality $f(x) < g(x)$, where $f(x) = [x]\cdot\{x\}$ and $g(x) = x - 1$, then for $0 \leq x \leq 3$, calculate the value of $d$.

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