
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 of the part bounded by two curves  $y=\sqrt{x},\ \sqrt{x}+\sqrt{y}=1$  and the  $x$ -axis.

1956 Tokyo Institute of Technology entrance exam

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