
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
Find the area bounded by the graph of  $ y\equal{}\sqrt[3]{x\plus{}\sqrt{x^2\plus{}1}}\plus{}\sqrt[3]{x\minus{}\sqrt{x^2\plus{}1}}$ , the line  $ x\minus{}y\minus{}1\equal{}0$  and the  $ x$  axis.

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