
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
\([a]\) represents the largest integer not greater than \(a\). For example, \(\left[2 \frac{1}{3}\right]=2\). Given that the sum of the roots of the equation \([3x + R] = 2x + \frac{3}{2}\) is \(S\), find the value of \(S\).

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