
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 sequence $\{a_n\}$ is an arithmetic sequence with the first term being $1$ and the common difference being $2$, and $\{b_n\}$ is a geometric sequence with the first term being $1$ and the common ratio being $2$, let $c_n=a_{b_n}$, $T_n=c_1+c_2+\ldots+c_n$ $(n\in\mathbb{N}^*)$, determine the minimum value of $n$ for which $T_n > 2013$.

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