
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
Given the set of inequalities about $x$: $$ \begin{cases} 1 \leqslant kx^{2} + 2 \\ x + k \leqslant 2 \end{cases} $$ There is a unique real number solution. Determine the set of real number values for $k$.

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