
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 $\overrightarrow{a}$ and $\overrightarrow{b}$ with an angle of $120^{\circ}$ between them, $|\overrightarrow{a}|=1$ and $|\overrightarrow{b}|=3$,
(I) Find the value of $|5\overrightarrow{a}-\overrightarrow{b}|$
(II) Find the cosine value of the angle between the vector $5\overrightarrow{a}-\overrightarrow{b}$ and $\overrightarrow{a}$.

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