
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
Calculate:<br/>$(1)8(2\overrightarrow{a}-\overrightarrow{b}+\overrightarrow{c})-6(\overrightarrow{a}-2\overrightarrow{b}+\overrightarrow{c})-2(2\overrightarrow{a}+\overrightarrow{c})$;<br/>$(2)\frac{1}{3}[\frac{1}{2}(2\overrightarrow{a}+8\overrightarrow{b})-(4\overrightarrow{a}-2\overrightarrow{b})]$.

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