
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 an arithmetic sequence $\{a_n\}$ where $a_1 = -1$ and the sum of the first 12 terms $S_{12} = 186$.

(Ⅰ) Find the general formula for the sequence $\{a_n\}$.

(Ⅱ) If sequence $\{b_n\}$ satisfies $b_{n} = \left( \frac{1}{2} \right)^{a_n}$, and the sum of the first $n$ terms of sequence $\{b_n\}$ is denoted as $T_n$, if the inequality $T_n < m$ holds for all $n \in \mathbb{N}^*$, find the range of the real number $m$.

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