
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
Given that $\overrightarrow{p}=x\overrightarrow{a}+y\overrightarrow{b}+z\overrightarrow{c}$, $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ is a basis of the space, and the coordinates of $\overrightarrow{p}$ in the basis $\{\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\}$ are (3,2,1), find the coordinates of $\overrightarrow{p}$ in the basis $\{\overrightarrow{a}-\overrightarrow{b},\overrightarrow{a}+\overrightarrow{b},\overrightarrow{c}\}$.

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