
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 line $x+y+2=0$ intersects the $x$-axis and $y$-axis at points $A$ and $B$ respectively. Point $P$ lies on the circle $(x-2)^2+y^2=2$. Find the range of the area of triangle $ABP$.

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