
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 $f(x)=A\sin (ωx+φ)+1$ where $A > 0$, $ω > 0$, and $- \frac {π}{2} < φ < \frac {π}{2}$. The function reaches its maximum value of $3$ at $x= \frac {π}{3}$. The distance between two adjacent symmetry axes of the function graph is $\frac {π}{2}$.
1. Find the analytical expression of the function $f(x)$,
2. If $x \in [0, \frac {π}{2}]$, find the range of $f(x)$.

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