
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 Cartesian coordinate system $xOy$, $\vec{i}, \vec{j}$ are the unit vectors parallel to the $x$-axis and $y$-axis, respectively. In the right triangle $\triangle ABC$, if $\vec{AB} = \vec{i} + \vec{j}$ and $\vec{AC} = 2\vec{i} + m\vec{j}$, find the value of the real number $m$.

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