
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
There exists a scalar $d$ such that
\[\mathbf{i} \times (\mathbf{v} \times 2\mathbf{i}) + \mathbf{j} \times (\mathbf{v} \times 2\mathbf{j}) + \mathbf{k} \times (\mathbf{v} \times 2\mathbf{k}) = d \mathbf{v}\] for all vectors $\mathbf{v}.$  Find $d$.

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