
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
In triangle ABC, which is an equilateral triangle with side length 3, it is known that vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ satisfy $\overrightarrow {AB}$=3 $\overrightarrow {a}$, $\overrightarrow {AC}$=3 $\overrightarrow {a}$$+ \overrightarrow {b}$. Among the following conclusions, the correct one is______. (Write out the numbers of all correct conclusions)
① $\overrightarrow {b}$ is a unit vector; ② $\overrightarrow {a}$ is a unit vector; ③ $\overrightarrow {a}$ ⊥ $\overrightarrow {b}$; ④ $\overrightarrow {b}$ ∥ $\overrightarrow {BC}$; ⑤ (6 $\overrightarrow {a}$+ $\overrightarrow {b}$) ⊥ $\overrightarrow {BC}$.

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