
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
Given $G=\frac{9x^2+21x+4m}{9}$ be the square of an expression linear in $x$, and valid when $x = p - 1$ where $p \neq 0$, determine the values of $m$ that satisfy these conditions.

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