
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 vectors $\overrightarrow{a}=(1+\sin 2x,\sin x-\cos x)$, $\overrightarrow{b}=(1,\sin x+\cos x)$, and the function $f(x)= \overrightarrow{a} \cdot \overrightarrow{b}$:

1. Find the maximum value of $f(x)$ and the corresponding value of $x$;
2. If $f(\theta)= \frac {8}{5}$, find the value of $\cos 2( \frac {\pi}{4}-2\theta)$.

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