
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
Determine the minimum possible value of $\Box$ such that $(ax+b)(bx+2a) = 36x^2 + \Box x + 72$, where $a$, $b$, and $\Box$ are distinct integers.

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