
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 all possible values of $x$ that could have been entered from the keyboard if the output value of $y$ is $1$ after running the following program:

$INPUT$ "Enter a real number in $[0,2\pi ]$"; $x$

$IF$ $x < 0$ $THEN$

$y=(x+1)\*(x+1)$

$ELSE$

$y=2\*\cos (x)$

$END$ $IF$

$PRINT$ $y$

$END$

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