
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
Define the length of the intervals (a, b), [a, b), (a, b], [a, b] to be d = b - a. Let $\lfloor x \rfloor$ denote the greatest integer less than or equal to x. For example, $\lfloor 3.2 \rfloor = 3$, $\lfloor -2.3 \rfloor = -3$. Denote $\{x\} = x - \lfloor x \rfloor$. Define $f(x) = \lfloor x \rfloor \cdot \{x\}$ and $g(x) = x - 1$. If the length of the interval, which is the solution set to the inequality $f(x) < g(x)$, is represented by d, determine the value of d when $0 \leq x \leq 3$.

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