
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  $A$ ,  $M$ , and  $C$  be nonnegative integers such that  $A+M+C=10$ . Find the maximum value of  $A\cdot M\cdot C+A\cdot M+M\cdot C+C\cdot A$.

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