
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 $$\overrightarrow {m} = (\sin x, \frac {3}{4})$$, $$\overrightarrow {n} = (\cos x, -1)$$, in triangle ABC, $\sin A + \cos A = \sqrt {2}$.  
(1) When $$\overrightarrow {m} \parallel \overrightarrow {n}$$, find the value of $\sin^2 x + \sin 2x$;  
(2) Let the function $f(x) = 2(\overrightarrow {m} + \overrightarrow {n}) \cdot \overrightarrow {n}$, find the value of $f(A)$.

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