
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 non-zero vectors $\overrightarrow {m}$ and $\overrightarrow {n}$, where $|\overrightarrow {n}|=2|\overrightarrow {m}|$ and $\overrightarrow {m} \perp (\sqrt {2}\overrightarrow {m}+\overrightarrow {n})$, find the angle between vectors $\overrightarrow {m}$ and $\overrightarrow {n}$.

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