
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
If for any $m \in (-2, -1)$, the function $f(x) = mx^2 - (5m+n)x + n$ has a root in the interval $x \in (3, 5)$, then the range of the real number $n$ is ______.

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