
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, point O is the origin, and the coordinates of three vertices of the parallelogram ABCD are A(2,3), B(-1,-2), and C(-2,-1).  
(1) Find the lengths of the diagonals AC and BD;  
(2) If the real number t satisfies $ (\vec{AB}+t\vec{OC})\cdot\vec{OC}=0 $, find the value of t.

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