
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 sequence $\{a_n\}$ with the general term formula $a_n = -2n + p$, and the sequence $\{b_n\}$ with the general term formula $b_n = 2^{n-7}$, let $c_n= \begin{cases} a_n, & \text{if } a_n \leqslant b_n \\ b_n, & \text{if } a_n > b_n \end{cases}$. If in the sequence $\{c_n\}$, $c_{10} > c_{n} (n \in \mathbb{N}^*, n \neq 10)$, then the range of values for the real number $p$ is \_\_\_\_\_\_.

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