
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
A right triangle has vertices at $A(0, 0)$, $B(a, 0)$, and $C(0, b)$ positioned on coordinate axes. The area of the triangle is 28 square units. If $b = 4$ and $a > 0$, find the value of $a$.

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