
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 \( a = \sqrt{3x+1} + \sqrt{3y+1} + \sqrt{3z+1} \) where \( x + y + z = 1 \) and \( x, y, z \geq 0 \). Find \( [a] \) (where \( [x] \) denotes the greatest integer less than or equal to the real number \( x \)).

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