
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 the given diagram, there are two squares $ABCD$ and $ADEF$ in space. $M$ and $N$ are the midpoints of $BD$ and $AE$, respectively. Among the following conclusions, select the correct ones (fill in all the correct conclusions corresponding to the numbers):

① $MN \perp AD$;

② $MN$ and $BF$ are skew lines;

③ $MN \parallel$ plane $ABF$;

④ The angle formed by $MN$ and $AB$ is $60^\circ$.

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