
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 $x$ with respect to the vectors $p$, $q$, and $r$:

$x = \{11, -1, 4\}$

$p = \{1, -1, 2\}$

$q = \{3, 2, 0\}$

$r = \{-1, 1, 1\}$

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