
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 that $$\overrightarrow{i}$$, $$\overrightarrow{j}$$, and $$\overrightarrow{k}$$ are three mutually perpendicular unit vectors, and a non-zero vector $$\overrightarrow{a}=a_{1}\overrightarrow{i}+a_{2}\overrightarrow{j}+a_{3}\overrightarrow{k}$$ (where $a_{1}$, $a_{2}$, $a_{3} \in \mathbb{R}$), if the angles between vector $$\overrightarrow{a}$$ and vectors $$\overrightarrow{i}$$, $$\overrightarrow{j}$$, $$\overrightarrow{k}$$ are respectively $\alpha$, $\beta$, $\gamma$, then $cos^{2}\alpha+cos^{2}\beta+cos^{2}\gamma=$ ______.

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