
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]


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Given that the sum of the first $n$ terms of an arithmetic sequence ${a_n}$ is ${S_n}$, ${a_5} + {a_6} = 24$, ${S_{11}} = 143$. The sum of the first $n$ terms of another sequence ${b_n}$ is ${T_n}$, which satisfies ${2^{{a_n} - 1}} = {T_n} - {a_1}\ (n \in {\mathbb{N}^*})$.

(1) Find the general term formula of the sequence ${a_n}$ and the sum of the first $n$ terms of the sequence ${\left\{ {\frac{1}{{{a_n}{a_{n + 1}}}}} \right\}}$.

(2) Determine whether the sequence ${b_n}$ is a geometric sequence and explain your reasoning.

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