
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 value of the following expressions without using a calculator:
\\((1)\\lg 5^{2}+ \frac {2}{3}\lg 8+\lg 5\lg 20+(\lg 2)^{2}\\)
\\((2)\\) Let \(2^{a}=5^{b}=m\), and \(\frac {1}{a}+ \frac {1}{b}=2\), find \(m\).

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