
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

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

$x = \{6, -1, 7\}$

$p = \{1, -2, 0\}$

$q = \{-1, 1, 3\}$

$r = \{1, 0, 4\}$

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