
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
Let  $a\in\mathbb{R}-\{0\}$ . Find all functions  $f: \mathbb{R}\to\mathbb{R}$  such that  $f(a+x) = f(x) - x$  for all  $x\in\mathbb{R}$ .

*Dan Schwartz*

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