
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 $xoy$, given points $A(1,4)$, $B(-2,3)$, and $C(2,-1)$.
- $(I)$ Calculate $\overrightarrow{AB} \cdot \overrightarrow{AC}$ and $|\overrightarrow{AB} + \overrightarrow{AC}|$;
- $(II)$ Let the real number $t$ satisfy $(\overrightarrow{AB} - t\overrightarrow{OC}) \perp \overrightarrow{OC}$, find the value of $t$.

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