
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 sets \( M = \left\{ x \mid x^{2} - 9 > 0 \right\} \) and \( N = \left\{ x \in \mathbf{Z} \mid x^{2} - 8x + a < 0 \right\} \). If the number of subsets of \( M \cap N \) is 4, then the range of the real number \( a \) is \(\qquad\).

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