
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
Consider the expression \[(x+y+z+w)^{10} + (x-y-z-w)^{10}\]where $w$ is another variable added to the original expression. Simplify this expression by expanding it and combining like terms. How many terms are in the simplified expression?

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