
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 a sequence $\{a_{n}\}$ that satisfies $a_{1}+2a_{2}+\ldots +2^{n-1}a_{n}=n\cdot 2^{n}$, let the sum of the first $n$ terms of the sequence $\{a_{n}-tn\}$ be denoted as $S_{n}$. If $S_{n}\leqslant S_{10}$ holds for all $n\in \mathbb{N}^{*}$, determine the range of real number $t$.

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