
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 the velocity of an object moving with variable speed in a straight line is $v(t) = \sqrt{t}$, where $t \in [0, a]$, and the displacement is 18, then the real number $a = \_\_\_\_\_\_$.

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