
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 parallelepiped $ABCD-A_{1}B_{1}C_{1}D_{1}$, where $AB=4$, $AD=3$, $AA_{1}=3$, $\angle BAD=90^{\circ}$, $\angle BAA_{1}=60^{\circ}$, $\angle DAA_{1}=60^{\circ}$, find the length of $AC_{1}$.

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