
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 that the angle between vectors $\overset{\to }{a}$ and $\overset{\to }{b}$ is $120^\circ$, and $|\overset{\to }{a}|=2,|\overset{\to }{b}|=1$.
(1) Find the value of $(2\overset{\to }{a}-\overset{\to }{b})\cdot\overset{\to }{a}$;
(2) Find the value of $|\overset{\to }{a}+2\overset{\to }{b}|$.

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