
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 the system of linear equations 
\[ \begin{array}{l} {x \plus{} 2y \plus{} 3z \equal{} a} 
{2x \plus{} y \minus{} 2z \equal{} b} 
{3x \plus{} y \plus{} 5z \equal{} c} \end{array}
\]
determine the smallest possible value of positive integer  $ n$, where $n$ is the greatest common divisor of $a,b,c$.

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