
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
Find the range of the real number $m$ so that the quadratic equation $x^{2}+(m-2)x+m+6=0$ satisfies the following conditions:
(1) One real root is greater than 2, and the other real root is less than 2;
(2) Both real roots are greater than 1.

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