
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 function $y=A\sin (\omega x+ \varphi )(A > 0, \omega > 0)$, the coordinates of a highest point on the graph is $(2,\sqrt{2})$, and the graph intersects the $x$-axis at point $(6,0)$ between this highest point and its adjacent lowest point. Determine the analytical expression of this function.

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