
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 three vectors in the plane, $\overrightarrow{a} = (3, 2)$, $\overrightarrow{b} = (-1, 2)$, $\overrightarrow{c} = (4, 1)$:

(Ⅰ) Find the real numbers $m$ and $n$ such that $\overrightarrow{a} = m\overrightarrow{b} + n\overrightarrow{c}$.

(Ⅱ) If vector $\overrightarrow{d}$ satisfies $(\overrightarrow{d} - \overrightarrow{c}) \parallel (\overrightarrow{a} + \overrightarrow{b})$ and $|\overrightarrow{d} - \overrightarrow{c}| = \sqrt{5}$, find the coordinates of vector $\overrightarrow{d}$.

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