
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 $c$ so that
\[\alpha\mathbf{i} \times (\mathbf{v} \times \mathbf{i}) + \beta\mathbf{j} \times (\mathbf{v} \times \mathbf{j}) + \gamma\mathbf{k} \times (\mathbf{v} \times \mathbf{k}) = c \mathbf{v}\] 
for all vectors $\mathbf{v}$, where $\alpha$, $\beta$, and $\gamma$ are constants. Find $c$ in terms of $\alpha$, $\beta$, and $\gamma$.

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