
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
Write the decomposition of the vector $x$ in terms of the vectors $p, q, r$:

$x=\{6 ; 12 ;-1\}$

$p=\{1 ; 3 ; 0\}$

$q=\{2 ;-1 ; 1\}$

$r=\{0 ;-1 ; 2\}$

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