
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 vectors $\overrightarrow {a} = (\sin x, \frac {3}{4})$ and $\overrightarrow {b} = (\cos x, -1)$.   
(1) When $\overrightarrow {a}$ is parallel to $\overrightarrow {b}$, find the value of $\tan(x - \frac {\pi}{4})$;  
(2) Let the function $f(x) = 2(\overrightarrow {a} + \overrightarrow {b}) \cdot \overrightarrow {b}$, when $x \in [0, \frac {\pi}{2}]$, find the range of $f(x)$.

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