
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
Joey wrote a system of equations on a blackboard, where each of the equations was of the form  $a + b = c$  or  $a \cdot b = c$  for some variables or integers  $a, b, c$ . Then Sean came to the board and erased all of the plus signs and multiplication signs, so that the board reads: $x\,\,\,\, z = 15$  $x\,\,\,\, y = 12$  $x\,\,\,\, x = 36$ If  $x, y, z$  are integer solutions to the original system, find the sum of all possible values of  $100x+10y+z$ .

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