
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 vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are not collinear, $\overrightarrow{a} \cdot \overrightarrow{b} \neq 0$, and $\overrightarrow{c} = \overrightarrow{a} - \left( \frac{\overrightarrow{a} \cdot \overrightarrow{a}}{\overrightarrow{a} \cdot \overrightarrow{b}} \right) \overrightarrow{b}$, calculate the angle between vectors $\overrightarrow{a}$ and $\overrightarrow{c}$.

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