
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
$\{\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\}$ is a basis of the space, where $\overrightarrow{p}=3\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}$. $\{\overrightarrow{a}+\overrightarrow{b},\overrightarrow{a}-\overrightarrow{b},\overrightarrow{c}\}$ is another basis of the space, where $\overrightarrow{p}=x(\overrightarrow{a}+\overrightarrow{b})+y(\overrightarrow{a}-\overrightarrow{b})+\overrightarrow{c}$. Find $x+y$.

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