
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 $$\overrightarrow {a} = (\sin(\theta- \frac {\pi}{4}), -1)$$, $$\overrightarrow {b} = (-1, 3)$$ where $\theta \in (0, \frac {\pi}{2})$, and $$\overrightarrow {a} \parallel \overrightarrow {b}$$.
(1) Find the value of $\sin\theta$;
(2) Given in $\triangle ABC$, $\angle A = \theta$, $BC = 2\sqrt {2} + 1$, find the maximum value of side $AC$.

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