
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 $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{c}$ be vectors such that $\|\mathbf{a}\| = 2,$ $\|\mathbf{b}\| = 3,$ and $\|\mathbf{a} + \mathbf{b}\| = 5.$ Additionally, the equation $\mathbf{c} = 2 \mathbf{a} + 3 \mathbf{b} + 4 (\mathbf{a} \times \mathbf{b})$ holds. Find $\mathbf{b} \cdot \mathbf{c}$.

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