
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 vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfying $|\overrightarrow{a}| = \sqrt{2}, |\overrightarrow{b}| = 1$, and for all real numbers $x$, $|\overrightarrow{a}+x\overrightarrow{b}| \geq |\overrightarrow{a}+\overrightarrow{b}|$ always holds, then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is __________.

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