
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
(1) Given vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfy $|\overrightarrow{a}|=|\overrightarrow{b}|=3$, and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $120^{\circ}$, find $|\overrightarrow{a}+\overrightarrow{b}|$ and $|2\overrightarrow{a}-\overrightarrow{b}|$;
(2) Given non-zero vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfy $\overrightarrow{a}+3\overrightarrow{b}$ is perpendicular to $7\overrightarrow{a}-5\overrightarrow{b}$, and $\overrightarrow{a}-4\overrightarrow{b}$ is perpendicular to $7\overrightarrow{a}-2\overrightarrow{b}$, find the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$.

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