
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
The equation \(7 x^{2}-(k+13) x+k^{2}-k-2=0\) (where \(k\) is a real number) has two real roots \(\alpha\) and \(\beta\), with \(0 < \alpha < 1\) and \(1 < \beta < 2\). Find the range of \(k\).

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