
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
Let point $P$ be a point inside $\triangle ABC$ (not including the boundary), and $\overrightarrow{PA}=m\overrightarrow{PB}+n\overrightarrow{PC}$ ($m,n\in \mathbb{R}$), then the range of values for $(m+1)^2+(n-1)^2$ is
A) $(0,2)$
B) $(0,5)$
C) $(1,2)$
D) $(1,5)$

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