
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 by how many times the number \((2014)^{2^{2014}} - 1\) is greater than the number written in the following form:
\[
\left(\left((2014)^{2^0} + 1\right) \cdot \left((2014)^{2^1} + 1\right) \cdot \left((2014)^{2^2} + 1\right) \ldots \cdot \left((2014)^{2^{2013}} + 1\right)\right) + 1.
\]

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