
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 $f(x)= \frac{A}{2}\cos (2\omega x+2\phi)+1+ \frac{A}{2} (\omega > 0,0 < \phi < \frac{\pi}{2})$ has a maximum value of $3$, the distance between two adjacent axes of symmetry of the graph of $f(x)$ is $2$, and the y-intercept is $2$. Find the expression for the function $f(x)$.

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