
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 point \((x, y)\) is selected uniformly at random from the unit square \(S = \{ (x, y) \mid 0 \leq x \leq 1, 0 \leq y \leq 1 \}\). If the probability that \((3x + 2y, x + 4y)\) is in \(S\) is \(\frac{a}{b}\), where \(a\) and \(b\) are relatively prime positive integers, compute \(100a + b\).

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