
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
A regular triangular prism has a triangle $ABC$ with side $a$ as its base. Points $A_{1}, B_{1}$, and $C_{1}$ are taken on the lateral edges and are located at distances of $a / 2, a, 3a / 2$ from the base plane, respectively. Find the angle between the planes $ABC$ and $A_{1}B_{1}C_{1}$.

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