
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
Let $\overrightarrow {e_{1}}$ and $\overrightarrow {e_{2}}$ be a set of basis vectors in a plane, and given $\overrightarrow {a}= \overrightarrow {e_{1}}+2 \overrightarrow {e_{2}}$ and $\overrightarrow {b}=- \overrightarrow {e_{1}}+ \overrightarrow {e_{2}}$, then the vector $\overrightarrow {e_{1}}+ \overrightarrow {e_{2}}$ can be expressed as a linear combination of another set of basis vectors $\overrightarrow {a}$ and $\overrightarrow {b}$. That is, $\overrightarrow {e_{1}}+ \overrightarrow {e_{2}}$ = ______ $\overrightarrow {a}$ + ______ $\overrightarrow {b}$.

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