
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
The ancient Indian mathematician Poṣagala posed the following problem in the book "Lilavati": A person gives alms to another person, starting with 2 shana (an ancient Indian currency unit) on the first day, and doubling it every day. How much will be given in total for a month? In this problem, considering a month to have 31 days, let the person give $a_{n}$ shana to the other person on the $n$th day (where $1\leqslant n\leqslant 31$, $n\in \mathbb{N}$), and let the sum of the first $n$ terms of the sequence $\{a_{n}\}$ be $S_{n}$. If the inequality ${S}_{n}-62＜{a}_{n+1}^{2}-t{a}_{n+1}$ always holds, then the range of the real number $t$ is ______.

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