
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 vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ that satisfy $|\overrightarrow {a}| = 1$, $|\overrightarrow {b}| = 2$, and $|\overrightarrow {a} - 2\overrightarrow {b}| = \sqrt{10}$, determine the value of $\overrightarrow {a} \cdot \overrightarrow {b}$ (the dot product of $\overrightarrow {a}$ and $\overrightarrow {b}$).

A) $\frac{3}{2}$
B) $\frac{7}{4}$
C) $- \frac{3}{2}$
D) $- \frac{7}{4}$

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