
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
In the Cartesian coordinate plane $(xOy)$, there are two points $A(\cos θ, \sqrt {2}\sin θ)$ and $B(\sin θ,0)$, where $θ∈R$.
(1) When $θ∈[0, \frac {π}{2}]$, find the maximum value of $| \overrightarrow{AB}|$.
(2) When $θ∈[0, \frac {π}{2}]$, and $| \overrightarrow{AB}|= \sqrt { \frac {5}{2}}$, find the value of $\sin (2θ+ \frac {5π}{12})$.

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