
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
Given in $\triangle ABC$, $\sin ^{2}A+\sin ^{2}C=\sin ^{2}B+\sin A\cdot\sin C$, and $H$ is the orthocenter of $\triangle ABC$, satisfying $\overrightarrow{BC}\cdot \overrightarrow{BH}=8$, calculate the area of $\triangle ABC$.

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