
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
A certain simple solid's diagonal length is $a$. In the front view, side view, and top view of this solid, the projection of this diagonal is a line segment with a length of $\sqrt{2}$. Calculate the value of $a$.

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