
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 a triangle with vertices A(0, 2), B(2, 0), and O(0, 0) is divided into two parts by the line $y = ax - a$, let the area of the part closer to the origin O be $S$. Write the expression for $S$ in terms of $a$.

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