
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 $|\vec{TM}|=2$, $|\vec{TN}|=4$, and $\vec{TM}\cdot \vec{TN}= \frac {5}{2}$, if point $P$ satisfies $|\vec{TM}+ \vec{TN}- \vec{TP}|=2$, then the range of $|\vec{TP}|$ is ______.

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