
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 $\mathbf{c}$ and $\mathbf{d}$ be vectors such that $\|\mathbf{c}\| = 3,$ $\|\mathbf{d}\| = 7,$ and $\|\mathbf{c} \times \mathbf{d}\| = 15.$ Find $|\mathbf{c} \cdot \mathbf{d}|.$

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