
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 $\overrightarrow{a} = (1, 0)$, $\overrightarrow{b} = (1, 2)$, $\overrightarrow{c} = (0, 1)$.

(Ⅰ) Find the real numbers $\lambda$ and $\mu$ such that $\overrightarrow{c} = \lambda \overrightarrow{a} + \mu \overrightarrow{b}$;

(Ⅱ) If $\overrightarrow{AB} = -\overrightarrow{a} + 3\overrightarrow{c}$, $\overrightarrow{AC} = 4\overrightarrow{a} - 2\overrightarrow{c}$, find the angle $\theta$ between vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$.

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