
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
Among the following statements:
① If $\overrightarrow {OA}+ \overrightarrow {OB}+ \overrightarrow {OC} = \overrightarrow {0}$, then point O is the centroid of $\triangle ABC$.
② If point O satisfies $|\overrightarrow {OA}|^{2}+|\overrightarrow {BC}|^{2}=|\overrightarrow {OB}|^{2}+|\overrightarrow {CA}|^{2}=|\overrightarrow {OC}|^{2}+|\overrightarrow {AB}|^{2}$, then point O is the orthocenter of $\triangle ABC$.
③ If a moving point P satisfies $\overrightarrow {OP}= \overrightarrow {OA}+\lambda\left( \frac { \overrightarrow {AB}}{|\overrightarrow {AB}|}+ \frac { \overrightarrow {AC}}{|\overrightarrow {AC}|}\right)(\lambda\in\mathbb{R})$, the trajectory of point P must pass through the incenter of $\triangle ABC$.
④ If a moving point P satisfies $\overrightarrow {OP}= \overrightarrow {OA}+\lambda\left( \frac { \overrightarrow {AB}}{|\overrightarrow {AB}|\sin B}+ \frac { \overrightarrow {AC}}{|\overrightarrow {AC}|\sin C}\right)(\lambda\in\mathbb{R})$, the trajectory of point P must pass through the centroid of $\triangle ABC$.
⑤ If a moving point P satisfies $\overrightarrow {OP}= \overrightarrow {OA}+\lambda\left( \frac { \overrightarrow {AB}}{|\overrightarrow {AB}|\cos B}+ \frac { \overrightarrow {AC}}{|\overrightarrow {AC}|\cos C}\right)(\lambda\in\mathbb{R})$, the trajectory of point P must pass through the circumcenter of $\triangle ABC$.
The correct statements are __________.

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