
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
Find the volume of the triangular pyramid formed by vectors $\overline{O A}$, $\overline{O B}$, and $\overline{O C}$, given $|\overrightarrow{O A}|=5$, $|\overrightarrow{O B}|=2$, $|\overrightarrow{O C}|=6$, $\overline{O A} \cdot \overrightarrow{O B}=0$, $\overline{O A} \cdot \overline{O C}=0$, and $\overline{O B} \cdot \overline{O C}=8$.

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