
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 point moving in the positive direction of the $OX$ axis has its horizontal coordinate given by $x(t) = 5(t + 1)^2 + \frac{a}{(t + 1)^5}$, where $a$ is a positive 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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