
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
Two numbers \(a\) and \(b\) with \(0 \leq a \leq 1\) and \(0 \leq b \leq 1\) are chosen at random. The number \(c\) is defined by \(c=2a + 2b\). The numbers \(a\), \(b\), and \(c\) are each rounded to the nearest integer to give \(A\), \(B\), and \(C\), respectively. Calculate the probability that \(2A + 2B = C\).

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