
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  $P$  be a point on the graph of the function  $y=x+\frac{2}{x}(x>0)$ .  $PA,PB$  are perpendicular to line  $y=x$  and  $x=0$ , respectively, the feet of perpendicular being  $A$  and  $B$ . Find the value of  $\overrightarrow{PA}\cdot \overrightarrow{PB}$ .

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