
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 $\overrightarrow{a} = (2,1)$, $\overrightarrow{b} = (-3,-4)$, and $\overrightarrow{c}$ is perpendicular to $\overrightarrow{a} - \overrightarrow{b}$.
1. Calculate $2\overrightarrow{a} + 3\overrightarrow{b}$ and the magnitude $|\overrightarrow{a} - 2\overrightarrow{b}|$;
2. If $\overrightarrow{c}$ is a unit vector, determine the coordinates of $\overrightarrow{c}$.

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