
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
Let $[a]$ represent the greatest integer less than or equal to $a$. For example,
$$
[\sqrt{2}] = 1, \quad [-\sqrt{2}] = -2.
$$

Find the sum of all roots of the equation $[3x + 1] = 2x - \frac{1}{2}$.

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