
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 \( p, q, r \):

\( x = \{8, -7, -13\} \)

\( p = \{0, 1, 5\} \)

\( q = \{3, -1, 2\} \)

\( r = \{-1, 0, 1\} \)

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