
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 $\overrightarrow {a}$, $\overrightarrow {b}$, $\overrightarrow {c}$, $\overrightarrow {d}$ that satisfy $| \overrightarrow {a} | = | \overrightarrow {b} | = 1$, and $\overrightarrow {a} \perp \overrightarrow {b}$. Let $\overrightarrow {c} = \overrightarrow {a} + (x - 3) \overrightarrow {b}$ and $\overrightarrow {d} = x \overrightarrow {a} + t \overrightarrow {b}$.

(I) If $| \overrightarrow {c} | = \sqrt {5}$, find the range of the real number $x$.
(II) If $\overrightarrow {c} || \overrightarrow {d}$, find the minimum value of the real number $t$.

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