
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 $\overrightarrow {a}$=(-3,2), $\overrightarrow {b}$=(2,1), $\overrightarrow {c}$=(3,-1), and t∈R.
(1) Find the minimum value of $| \overrightarrow {a}+t \overrightarrow {b}|$ and the corresponding t value;
(2) If $\overrightarrow {a}-t \overrightarrow {b}$ is collinear with $\overrightarrow {c}$, find the real number t.

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