
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 the function
\[ x(t)=5(t+1)^{2}+\frac{a}{(t+1)^{5}}, \]
where \( a \) is a constant. Find the minimum value of \( a \) such that \( x(t) \geqslant 24 \) for all \( t \geqslant 0 \).

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