
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 the region $D$ in the Cartesian coordinate system $xOy$ is defined by the system of inequalities $\begin{cases} 0\leqslant x\leqslant \sqrt{2}, \\ y\leqslant 2, \\ x\leqslant \sqrt{2}y \end{cases}$, if $M(x, y)$ is a moving point in $D$ and the coordinates of point $A$ are $(\sqrt{2},1)$, calculate the maximum value of $z = \overrightarrow{OM}\cdot\overrightarrow{OA}$.

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