
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 inequality in $x$: 
$$\left[\left(k^{2}+6 k+14\right) x-9\right]\left[\left(k^{2}+28\right) x-2 k^{2}-12 k\right]<0,$$
the solution set $M$ intersects with the set of integers $\mathbf{Z}$ such that $M \cap \mathbf{Z}=\{1\}$. Find the range of values for the constant $k$.

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