
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 the explicit formula for the sequence $\{a_n\}$ as $a_n = -n + p$ and the explicit formula for the sequence $\{b_n\}$ as $b_n = 2^{n-5}$, define the sequence $\{c_n\}$ as follows:

$$
c_n = 
\begin{cases} 
a_n, & \text{if } a_n \leq b_n \\ 
b_n, & \text{if } a_n > b_n
\end{cases}
$$

If in the sequence $\{c_n\}$, $c_8 > c_n$ for all $n \in \mathbb{N}^*$ and $n \neq 8$, determine the range of the real number $p$.

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