
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
In the Cartesian coordinate system $xOy$, circle $C$: $x^{2}+y^{2}=4$ intersects the positive half of the $x$-axis and the negative half of the $y$-axis at points $M$ and $N$ respectively. If point $P$ is any point on circle $C$, then the maximum value of $\overrightarrow{PM}\cdot \overrightarrow{PN}$ is \_\_\_\_\_\_.

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