
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 $d=b-a$. The length of the union of multiple intervals is the sum of the lengths of each interval. Let $f(x)=[x]\{x\}$ and $g(x)=x-1$. When $0 \leq x \leq k$, the length of the solution interval for the inequality $f(x) < g(x)$ is 5, find the value of $k$.

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