
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
For any real numbers $a$ and $b$, given that $|a-b| \leqslant 1$, $|2a-1| \leqslant 1$, and it always holds that $|4a-3b+2| \leqslant m$, find the range of values for the real number $m$.

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