
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 the planar vectors $\overrightarrow{a}$ and $\overrightarrow{b}$, where $|\overrightarrow{a}| = 1$ and $|\overrightarrow{b}| = 2$, and $|\overrightarrow{a} - \overrightarrow{b}| = \sqrt{7}$.

1. Find the angle θ between $\overrightarrow{a}$ and $\overrightarrow{b}$.
2. If $\overrightarrow{c} = t\overrightarrow{a} + \overrightarrow{b}$ and $\overrightarrow{a} \perp \overrightarrow{c}$, find the value of $t$ and $|\overrightarrow{c}|$.

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