
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 $f(x)=A\sin (\omega x)+b$ ($A > 0$, $\omega > 0$) has a maximum value of $2$ and a minimum value of $0$, and the distance between two adjacent axes of symmetry of its graph is $2$, then $f(1)+f(2)+\ldots+f(2008)=$ \_\_\_\_\_\_.

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