
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
Consider the following propositions:
① The direction vector of line $l$ is $\overrightarrow{a} = (1, -1, 2)$, the direction vector of line $m$ is $\overrightarrow{b} = (2, 1, -\frac{1}{2})$, therefore, line $l$ is perpendicular to line $m$;
② The direction vector of line $l$ is $\overrightarrow{a} = (0, 1, -1)$, and the normal vector of plane $\alpha$ is $\overrightarrow{n} = (1, -1, -1)$, thus line $l$ is perpendicular to plane $\alpha$;
③ The normal vectors of planes $\alpha$ and $\beta$ are respectively $\overrightarrow{n_1} = (0, 1, 3)$ and $\overrightarrow{n_2} = (1, 0, 2)$, therefore, $\alpha$ is parallel to $\beta$;
④ Plane $\alpha$ passes through three points A$(1, 0, -1)$, B$(0, 1, 0)$, and C$(-1, 2, 0)$. If vector $\overrightarrow{n} = (1, u, t)$ is the normal vector of plane $\alpha$, then $u + t = 1$.
Indicate which of the above propositions are true. Fill in the indexes of the correct propositions.

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