
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
What is the smallest area that triangle \( OAB \) can have if its sides \( OA \) and \( OB \) lie on the graph of the function \( y=2|x|-x+1 \), and the line \( AB \) passes through the point \( M(0, 2) \)?

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