
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 two vectors in space, $\overrightarrow {a}=(2,-y,2)$ and $\overrightarrow {b}=(4,2,x)$, with the condition that the sum of their squared magnitudes equals 44, i.e., $|\overrightarrow {a}|^2 + |\overrightarrow {b}|^2 = 44$, and that $\overrightarrow {a}$ is perpendicular to $\overrightarrow {b}$, with $x, y \in \mathbb{R}$, find the value of $x + y$.

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