
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
Consider a complex number $z=-3\cos \theta + 2i\sin \theta$:
1. When $\theta= \frac {4}{3}\pi$, find the value of $|z|$.
2. If the point corresponding to the complex number $z$ lies on the line $x+3y=0$, calculate the value of $\frac {2\cos^{2} \frac {\theta}{2}-1}{ \sqrt {2}\sin(\theta+ \frac {\pi}{4})}$.

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