
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 the base and height of a triangle are in an arithmetic progression, and the base is \(2a - d\) while the height is \(2a + d\), where \(d\) is the common difference and \(a\) is a positive number, determine the area of the triangle.

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