
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 vectors $\overrightarrow {a} = (3, 2)$, $\overrightarrow {b} = (-1, 2)$, and $\overrightarrow {c} = (4, 1)$,
1. Find the magnitude of $3\overrightarrow {a} + \overrightarrow {b} - \overrightarrow {c}$.
2. Find the real numbers $m$ and $n$ that satisfy the condition $\overrightarrow {a} = m\overrightarrow {b} + n\overrightarrow {c}$.
3. If vector $\overrightarrow {d}$ satisfies $(\overrightarrow {d} - \overrightarrow {c}) \parallel (\overrightarrow {a} + \overrightarrow {b})$ and $|\overrightarrow {d} - \overrightarrow {c}| = 1$, find $\overrightarrow {d}$.

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