
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 vector \( x \) in terms of the vectors \( p, q, r \):

\[ x = \{13, 2, 7\} \]

\[ p = \{5, 1, 0\} \]

\[ q = \{2, -1, 3\} \]

\[ r = \{1, 0, -1\} \]

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