
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 two non-collinear vectors $\overrightarrow {e_{1}}$ and $\overrightarrow {e_{2}}$, $\overrightarrow {a} = \overrightarrow {e_{1}} + \overrightarrow {e_{2}}$, $\overrightarrow {b} = 2\overrightarrow {e_{1}} - \overrightarrow {e_{2}}$, $\overrightarrow {c} = \overrightarrow {e_{1}} + 2\overrightarrow {e_{2}}$. Express $\overrightarrow {c}$ in terms of the basis vectors $\overrightarrow {a}$ and $\overrightarrow {b}$.

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