
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
If $a$ and $b$ are the solutions of the equation $x + \lg x = 4$, and $x + 10^x = 4$, respectively, and the function $f(x) = \begin{cases} x^{2}+(a+b)x+2, & x\leq0 \\ 2, & x>0\end{cases}$, then the number of solutions to the equation $f(x) = x$ is \_\_\_\_\_\_.

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