
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 $\overrightarrow{a}=(1,2)$, $\overrightarrow{b}=(-1,1)$, and $\overrightarrow{c}= \overrightarrow{a}+\lambda \overrightarrow{b}$. If $\overrightarrow{a} \perp \overrightarrow{c}$, then the value of the real number $\lambda$ is \_\_\_\_\_\_.

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