
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 that the sum of all coefficients in the expansion of $(x+ \frac {1}{x})^{2n}$ is greater than the sum of all coefficients in the expansion of $(3 3x -x)^{n}$ by $240$.
$(1)$ Find the constant term in the expansion of $(x+ \frac {1}{x})^{2n}$ (answer with a number);
$(2)$ Find the sum of the binomial coefficients in the expansion of $(2x- \frac {1}{x})^{n}$ (answer with a number)

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