
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
Let vectors $\overrightarrow {a} = (\sqrt {3}\sin x, \sin x)$ and $\overrightarrow {b} = (\cos x, \sin x)$, where $x \in [0, \frac {\pi}{2}]$  
(1) If $|\overrightarrow {a}| = |\overrightarrow {b}|$, find the value of $x$;  
(2) Let the function $f(x) = \overrightarrow {a} \cdot \overrightarrow {b}$, find the range of $f(x)$.

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