
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 that $\theta$ is an angle in the first quadrant, $\overrightarrow {a}$ = (sin($\theta$ - $\pi$), 1), and $\overrightarrow {b}$ = (sin($\frac {\pi}{2}$ - $\theta$), - $\frac {1}{2}$).

(1) If $\overrightarrow {a}$ and $\overrightarrow {b}$ are collinear, find the value of $\frac {sin\theta+cos\theta}{sin\theta -cos\theta }$.

(2) If $|$ $\overrightarrow {a}$ + $\overrightarrow {b}$ $|$ = 1, find the value of $sin\theta+cos\theta$.

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