
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
If $\overrightarrow {a} = (0,3)$, $\overrightarrow {b} = (\sqrt {3},1)$, $\overrightarrow {c} = 3 \overrightarrow {a} +5 \overrightarrow {b}$, $\overrightarrow {d} = m \overrightarrow {a} -5 \overrightarrow {b}$,  
(1) For what value of $m$ are $\overrightarrow {c}$ and $\overrightarrow {d}$ parallel to each other;  
(2) For what value of $m$ are $\overrightarrow {c}$ and $\overrightarrow {d}$ perpendicular to each other.

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