
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
Determine the total number of different values that the elements of the matrix can take, where $c_{ij} = 2^i - 1 \cdot 2^j - 1 + 2^i - 1 + 2^j - 1 = 2^{i + j} - 1 + 2^{i + 1} - 2 + 2^{j + 1} - 2$ (where $i=1, 2, \ldots, 7$; $j=1, 2, \ldots, 12$).

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