
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 $\overset{⇀}{a}$ and $\overset{⇀}{b}$ that satisfy $|\overset{⇀}{a}| = 4$, $|\overset{⇀}{b}| = 3$, and the angle between $\overset{⇀}{a}$ and $\overset{⇀}{b}$, denoted by $θ$, is $60^{\circ}$.

(1) Find the value of $(\overset{⇀}{a} + 2\overset{⇀}{b}) \cdot (2\overset{⇀}{a} - \overset{⇀}{b})$;

(2) Find the value of $|2\overset{⇀}{a} - \overset{⇀}{b}|$.

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