
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
Let a function $h$ be defined on $[1,4]$ with values ranging from $[0,1]$. Define a new function $k(x)$ as follows:
\[k(x) = (1 - h(x-1))^2.\]
Determine the domain and range of $k(x)$, and report the results as an ordered quadruple $(a, b, c, d)$.

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