
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 $(xOy)$, $\overrightarrow{i}$ and $\overrightarrow{j}$ are the unit vectors in the directions of the $x$-axis and $y$-axis respectively. Given $\overrightarrow{OA} = \overrightarrow{i} + 2\overrightarrow{j}$, $\overrightarrow{OB} = 3\overrightarrow{i} + 4\overrightarrow{j}$, and $\overrightarrow{OC} = 2t\overrightarrow{i} + (t + 5)\overrightarrow{j}$, if $\overrightarrow{AB}$ and $\overrightarrow{AC}$ are collinear, find the value of the real number $t$.

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