
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
When $$θ= \frac {4}{3}π$$, find the value of $|z|$;  
If the complex number $z$ corresponds to a point on the line $x+3y=0$, calculate the value of $$\frac {2\cos^{2} \frac {θ}{2}-1}{ \sqrt {2}\sin(θ+ \frac {π}{4})}$$.

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