
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 \(\mathbf{a}, \mathbf{b},\) and \(\mathbf{c}\) such that \(\|\mathbf{a}\| = \|\mathbf{b}\| = 1\), \(\|\mathbf{a} + \mathbf{b}\| = 2\), and
\[
\mathbf{c} - \mathbf{a} - 2\mathbf{b} = 4 (\mathbf{a} \times \mathbf{b}),
\]
find \(\mathbf{b} \cdot \mathbf{c}\).

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